mathematical existence process also called brownian motion process brownian motion due historical connection model brownian movement liquids ref name brush page ref ref name applebaum page ref ref name gikhmanskorokhod page ref red playing central role theory probability wiener process often considered important studied stochastic process connections stochastic processes ref name doob stochasticp ref name rogerswilliams page ref name steele page ref ref name florescu page ref ref name karlintaylor page ref ref name karatzasshreve pageviii ref ref name revuzyor pageix ref index set state space non negative numbers real numbers respectively continuous index set states space ref name rosenthal page ref process defined


generally state space math n math dimensional euclidean space ref name klebaner page ref name karlintaylor page mean increment zero resulting wiener brownian motion process said zero drift mean increment two points time equal time difference multiplied constant math mu math real number resulting stochastic process said drift math mu math ref name steele page ref ref name rtersperes page ref name karatzasshreve page ref almost surely sample path wiener process continuous everywhere nowhere differentiable considered continuous

Formal science
Mathematics
Pure mathematics
Probability theory
Stochastic process


version simple random walk ref name applebaum page ref ref name rtersperes page ref process arises mathematical limit stochastic processes certain random walks rescaled ref name karatzasshreve page ref ref name shreve page ref subject donsker 's theorem invariance principle also known functional central limit theorem ref name kallenberg page ref ref name karatzasshreve page ref ref name rtersperes page ref wiener process member important families stochastic processes including markov processes l vy processes gaussian processes ref name rogerswilliams page ref name applebaum page process also many applications main stochastic process used stochastic calculus ref name klebaner ref ref name karatzasshreve page ref plays central role quantitative finance ref name applebaum page ref ref name karlintaylor page ref


used example black scholes merton model ref name klebaner page ref process also used different fields including majority natural sciences well branches social sciences mathematical model various random phenomena ref name steele page ref name karatzasshreve page ref ref name wiersema page ref poisson process poisson process stochastic process different forms definitions ref name tijms page ref ref name daleyvere jones chap ref defined counting process stochastic process represents random number points events time number points process located interval


name applebaum page homogeneous poisson process defined generalized different ways defined index set real line stochastic process also called stationary poisson process ref name kingman page ref ref name daleyvere jones page ref parameter constant poisson process replaced non negative integrable function math math resulting process called inhomogeneous nonhomogeneous poisson process average density points process longer constant ref name kingman page ref serving fundamental process queueing theory poisson process important process mathematical models


finds applications models events randomly occurring certain time windows ref name karlintaylor page ref ref name kleinrock page ref defined real line poisson process interpreted stochastic process ref name applebaum page ref name rosenblatt page ref among random objects ref name haenggi page ref ref name chiustoyan page ref defined math n math dimensional euclidean space mathematical spaces ref name kingman page ref often interpreted random set random counting measure instead stochastic process ref name haenggi page ref name chiustoyan page setting poisson process also called poisson point process one important objects probability theory applications


theoretical reasons ref name stirzaker ref name streit page ref remarked poisson process receive much attention partly due often considered real line mathematical spaces ref name streit page ref name kingman pagev ref definitions stochastic process stochastic process defined collection random variables defined common probability space math omega mathcal f p math math omega math sample space math mathcal f math math sigma math algebra math p math probability measure random variables indexed set math math take values mathematical space math math


must measurable respect math sigma math algebra math sigma math ref name lamperti page words given probability space math omega mathcal f p math measurable space math sigma math stochastic process collection math math valued random variables written ref name florescu page ref center math x math center historically many problems natural sciences point math math meaning time math x math random variable representing value observed time math math ref name borovkov page ref stochastic process also written math x omega math reflect actually function


line natural numbers interval giving set math math interpretation time ref name doob stochasticp addition sets index set math math another set total order general set ref name doob stochasticp ref name billingsley page ref cartesian plane math r math math n math dimensional euclidean space element math math represent point space ref name karlintaylor page ref said many results theorems possible stochastic processes totally ordered index set ref name skorokhod page ref state space mathematical space math math stochastic process called ' 'state space''


mathematical space defined using integers real lines math n math dimensional euclidean spaces complex planes abstract mathematical spaces state space defined using elements reflect different values stochastic process take ref name doob stochasticp ref name gikhmanskorokhod page ref name lamperti page ref name florescu page ref ref name br maud page ref sample function '' 'sample function''' single outcome stochastic process formed taking single possible value random variable stochastic process ref name lamperti page ref name florescu page ref precisely math x omega math stochastic process point math omega omega math mapping center math x cdot omega rightarrow math center


called sample function '' 'realization''' particularly math math interpreted time '' 'sample path''' stochastic process math x omega math ref name rogerswilliams page b ref means fixed math omega omega math exists sample function maps index set math math state space math math ref name lamperti page names sample function stochastic process include '''trajectory''' '''path function''' ref name billingsley page ref '''path''' ref name ksendal page ref increment '''increment''' stochastic process difference two random variables stochastic process stochastic process index set interpreted time


x b omega omega x omega b math center law math x math written ref name lamperti page center math mu b p omega omega x omega b math center law stochastic process random variable also called '''probability law''' '''probability distribution''' '' 'distribution''' ref name borovkov page ref name frizvictoir page ref name whitt page ref ref name applebaumbook page ref ref name revuzyor page ref finite dimensional probability distributions stochastic process math x math law math mu math '''finite dimensional distribution''' math dotst n math defined center math mu dotst n p circ x dots x n math center measure math mu n math joint distribution random vector math x dots x n math viewed projection law


math mu math onto finite subset math math ref name kallenberg page ref name rogerswilliams page ref measurable subset math c math math n math fold cartesian power math n times dots times math finite dimensional distributions stochastic process math x math written ref name lamperti page center math mu dotst n c p big big omega omega big x omega dots x n omega big c big big math center finite dimensional distributions stochastic process satisfy two mathematical conditions known consistency conditions ref name rosenthal page stationarity '''stationarity''' mathematical property stochastic process random variables stochastic process identically distributed words math x math stationary stochastic process


math math random variable math x math distribution means set math n math index set values math dots n math corresponding math n math random variables center math x dots x n math center probability distribution index set stationary stochastic process usually interpreted time integers real line ref name lamperti page ref ref name gikhmanskorokhod page ref concept stationarity also exists point processes random fields index set interpreted time ref name lamperti page ref name adler page ref ref name chiustoyan page ref index set math math interpreted


time stochastic process said stationary finite dimensional distributions invariant translations time type stochastic process used describe physical system steady state still experiences random fluctuations ref name lamperti page intuition behind stationarity time passes distribution stationary stochastic process remains ref name doob page ref sequence random variables forms stationary stochastic process random variables identically distributed ref name lamperti page stochastic process definition stationarity sometimes said strictly stationary


forms stationarity one example discrete time continuous time stochastic process math x math said stationary wide sense process math x math finite second moment math math covariance two random variables math x math math x h math depends number math h math math math ref name doob page ref name florescu page ref khinchin introduced related concept '' 'stationarity wide sense''' names including '''covariance stationarity''' '' 'stationarity broad sense''' ref name florescu page ref name gikhmanskorokhod page ref filtration filtration increasing sequence sigma algebras defined relation


probability space index set total order relation case index set subset real numbers formally stochastic process index set total order filtration math mathcal f math probability space math omega mathcal f p math family sigma algebras math mathcal f subseteq mathcal f subseteq mathcal f math math leq math math math math leq math denotes total order index set math math ref name florescu page concept filtration


possible study amount information contained stochastic process math x math math math interpreted time math math ref name florescu page ref name williams page intuition behind filtration math mathcal f math time math math passes information math x math known available captured math mathcal f math resulting finer finer partitions math omega math ref name klebaner page ref ref name rtersperes page ref modification '''modification''' stochastic process another stochastic process closely related original stochastic process precisely stochastic process math x math index set math math set space math math


probability space math omega cal f p math another stochastic process math math said modification math math math math following center math p x math center holds two stochastic processes modifications finite dimensional law ref name rogerswilliams page ref said '' 'stochastically equivalent''' '''equivalent''' ref name borovkov page ref instead modification term '' 'version''' also used ref name adler page ref name klebaner page ref ref name ksendal page ref ref name florescu page ref however authors use term version two stochastic processes finite dimensional distributions may defined different probability spaces two processes modifications


also versions latter sense converse ref name revuzyor page ref ref name frizvictoir page continuous time real valued stochastic process meets certain moment conditions increments kolmogorov continuity theorem says exists modification process continuous sample paths probability one stochastic process continuous modification version ref name ksendal page ref name florescu page ref name applebaumbook page ref theorem also generalized random fields index set math n math dimensional euclidean space ref name kunita page ref well stochastic processes metric spaces state spaces ref name kallenberg page ref indistinguishable two


stochastic processes math x math math math defined probability space math omega mathcal f p math index set math math set space math math said '''indistinguishable''' following center math p x text math center holds ref name frizvictoir page ref name rogerswilliams page two math x math math math modifications almost surely continuous math x math math math indistinguishable ref name jeanblancyor page ref separability '''separability''' property stochastic process based index set relation probability measure property assumed functionals stochastic processes random


fields uncountable index sets form random variables stochastic process separable addition conditions index set must separable space means index set dense countable subset ref name adler page ref name ito page ref precisely real valued continuous time stochastic process math x math probability space math omega cal f p math separable index set math math dense countable subset math u subset math set math omega subset omega math probability zero math p omega math every open set math g subset math every closed set math f subset textstyle r infty infty math


two events math x f text g cap u math math x f text g math differ subset math omega math ref name gikhmanskorokhod page ref ref name todorovic page ref ref name molchanov page ref definition separability ref ref name borovkov page ref also stated index sets state spaces ref name gusakkukush page p ref case random fields index set well state space math n math dimensional euclidean space ref name adlertaylor page ref name adler page concept separability stochastic process introduced joseph doob ref


name ito page underlying idea separability make countable set points index set determine properties stochastic process ref name billingsley page stochastic process countable index set already meets separability conditions discrete time stochastic processes always separable ref name doob page ref theorem doob sometimes known doob 's separability theorem says real valued continuous time stochastic process separable modification ref name ito page ref name todorovic page ref name khoshnevisan page ref versions theorem also exist general stochastic processes index sets state spaces real line ref name skorokhod page independence two stochastic processes math x math


math math defined probability space math omega mathcal f p math index set math math said '''independent''' math n mathbb n math every choice epochs math ldotst n math random vectors math left x ldotsx n right math math left ldotsy n right math independent ref name lapidoth lapidoth amos ''a foundation digital communication'' cambridge university press ref uncorrelatedness two stochastic processes math left x right math math left right math called '''uncorrelated''' cross covariance math operatorname k mathbf x mathbf operatorname e left left x mu x right left mu right right math zero times ref name kunilpark kun il park fundamentals probability stochastic processes applications communications


real line math math math infty math take values real line metric space ref name whitt page ref ref name gusakkukush page p ref ref name bogachev vol page ref functions known c dl g cadlag functions based acronym french phrase ''continue droite limite gauche'' ref name whitt page ref name klebaner page ref skorokhod function space introduced anatoliy skorokhod ref name bogachev vol page often denoted letter math math ref name whitt page ref name gusakkukush page ref name bogachev vol page ref name klebaner page function space also referred space math math ref name whitt page ref name asmussen page ref ref name billingsley page ref notation function space also include interval c dl g functions


defined example math math denotes space c dl g functions defined unit interval math math ref name klebaner page ref name billingsley page ref name bass page ref skorokhod function spaces frequently used theory stochastic processes often assumed sample functions continuous time stochastic processes belong skorokhod space ref name bogachev vol page ref name asmussen page spaces contain continuous functions correspond sample functions wiener process space also functions discontinuities means sample functions stochastic processes jumps poisson process real line also members space ref


name billingsley page ref name binghamkiesel page ref regularity context mathematical construction stochastic processes term '' 'regularity''' used discussing assuming certain conditions stochastic process resolve possible construction issues ref name borovkov page ref ref name khoshnevisan page ref example study stochastic processes uncountable index sets assumed stochastic process adheres type regularity condition sample functions continuous ref name todorovic page ref ref name whitt page ref examples markov processes chains markov processes stochastic processes traditionally discrete continuous time markov property means next value markov process depends


current value conditionally independent previous values stochastic process words behavior process future stochastically independent behavior past given current state process ref name serfozo page ref ref name rozanov page ref brownian motion process poisson process one dimension examples markov processes ref name ross page ref continuous time random walks integers gambler 's ruin problem examples markov processes discrete time ref name florescu page ref ref name karlintaylor page ref markov chain type markov process either discrete


state space discrete index set often representing time precise definition markov chain varies ref name asmussen page ref example common define markov chain markov process either discrete continuous time countable state space thus regardless nature time ref name parzen page ref ref name karlintaylor page ref ref name lamperti chap ref ref name ross page ref also common define markov chain discrete time either countable continuous state space thus regardless state space ref name asmussen page argued first definition markov chain


discrete time tends used despite second definition used researchers like joseph doob kai lai chung ref name meyntweedie ref markov processes form important class stochastic processes applications many areas ref name latoucheramaswami ref name karlintaylor page ref example basis general stochastic simulation method known markov chain monte carlo used simulating random objects specific probability distributions found application bayesian statistics ref name rubinsteinkroese page ref ref name gamermanlopes ref concept markov property originally stochastic processes continuous discrete time property


adapted index sets math n math dimensional euclidean space results collections random variables known markov random fields ref name rozanov page ref ref name bremaud page ref martingale martingale discrete time continuous time stochastic process property every instant given current value past values process conditional expectation every future value equal current value discrete time property holds next value holds future values exact mathematical definition martingale requires two conditions coupled mathematical concept


filtration related intuition increasing available information time passes martingales usually defined real valued ref name klebaner page ref ref name karatzasshreve page ref ref name williams page ref also complex valued ref name doob page ref even general ref name pisier ref symmetric random walk wiener process zero drift examples martingales respectively discrete continuous time ref name klebaner page ref name karatzasshreve page sequence independent identically distributed random variables math x x x dots math zero mean stochastic process formed successive partial sums math x x x x x x dots math discrete time martingale ref name steele page ref


statistics particularly statistical inference ref name glassermankou ref found applications areas probability theory queueing theory palm calculus ref name baccellibremaud ref fields economics ref name hallheyde pagex ref finance ref name musielarutkowski l vy process l vy processes types stochastic processes considered generalizations random walks continuous time ref name applebaum page ref name bertoin pageviii ref processes many applications fields finance fluid mechanics physics biology ref name applebaum page ref ref name applebaumbook page ref main defining characteristics processes stationarity independence properties known ''processes stationary independent increments'' words


stochastic process math x math l vy process math n math non negatives numbers math leq leq dots leq n math corresponding math n math increments center math x x dots x n x n math center independent distribution increment depends difference time ref name applebaum page l vy process defined state space abstract mathematical space banach space processes often defined take values euclidean space index set non negative numbers math infty math gives interpretation


time important stochastic processes wiener process homogeneous poisson process one dimension subordinators l vy processes ref name applebaum page ref name bertoin pageviii random field random field collection random variables indexed math n math dimensional euclidean space manifold general random field considered example stochastic random process index set necessarily subset real line ref name adlertaylor page convention indexed collection random variables called random field index two dimensions ref name gikhmanskorokhod page ref


name lamperti page ref name koralovsinai page ref specific definition stochastic process requires index set subset real line random field considered generalization stochastic process ref name applebaumbook page ref point process point process collection points randomly located mathematical space real line math n math dimensional euclidean space abstract spaces sometimes term ''point process'' preferred historically word ''process'' denoted evolution system time point process also called '''random point field''' ref name chiustoyan page ref different


defined real line math n math dimensional euclidean space ref name karlintaylor page ref ref name schmidt page ref stochastic processes renewal counting processes studied theory point processes ref name daleyvere jones ref ref name coxisham page history early probability theory probability theory origins games chance long history games played thousands years ago ref name ref ref name david ref little analysis done terms probability ref name ref name maistrov page ref year often considered birth probability theory french mathematicians pierre fermat blaise pascal


written correspondence probability motivated gambling problem ref name ref name seneta page ref ref name tabak page ref earlier mathematical work done probability gambling games ''liber de ludo aleae'' gerolamo cardano written th century posthumously published later ref name ref name bellhouse ref cardano jakob bernoulli ref wrote ars conjectandi considered significant event history probability theory ref name bernoulli 's book published also posthumously inspired many mathematicians study probability ref name ref name maistrov page ref ref name tabak page ref despite renowned mathematicians contributing probability theory


pierre simon laplace abraham de moivre carl gauss sim poisson pafnuty chebyshev ref name chung ref ref name bingham ref mathematical community ref consider probability theory part mathematics th century ref name chung ref name benzibenzi ref name doob ref ref name cramer ref statistical mechanics physical sciences scientists developed th century discipline statistical mechanics physical systems containers filled gases regarded treated mathematically collections many moving particles although attempts incorporate randomness statistical physics scientists rudolf clausius work little


randomness ref name truesdell page ref ref name brush page ref changed james clerk maxwell contributed significantly field specifically kinetic theory gases presenting work assumed gas particles move random directions random velocities ref name truesdell page ref ref name brush ref kinetic theory gases statistical physics continued developed second half th century work done chiefly clausius ludwig boltzmann josiah gibbs would later influence albert einstein 's mathematical model brownian movement ref name brush page ref measure theory probability theory international congress mathematicians


paris david hilbert presented list mathematical problems sixth problem asked mathematical treatment physics probability involving axioms ref name bingham around start th century mathematicians developed measure theory branch mathematics studying integrals mathematical functions two founders french mathematicians henri lebesgue mile borel another french mathematician paul l vy published first probability book used ideas measure theory ref name bingham fundamental contributions probability theory made soviet union mathematicians sergei bernstein


aleksandr khinchin ref andrei kolmogorov ref name cramer kolmogorov published first attempt presenting mathematical foundation based measure theory probability theory ref name kendallbatchelor page ref early khinchin kolmogorov set probability seminars attended researchers eugene slutsky nikolai smirnov ref name vere jones page ref khinchin gave first mathematical definition stochastic process set random variables indexed real line ref name doob ref name vere jones page ref ref birth modern probability theory andrei kolmogorov published german book foundations probability theory titled ''grundbegriffe der wahrscheinlichkeitsrechnung''


connecting markov processes potential theory significant effect theory l vy processes led interest studying markov processes methods developed ref name jarrowprotter ref name bertoin pageviiiandix ref ref name steele page ref doob published book ''stochastic processes'' strong influence theory stochastic processes stressed importance measure theory probability ref name meyer ref name bingham ref doob also chiefly developed theory martingales later substantial contributions paul andr meyer earlier work carried sergei bernstein paul l vy jean ville latter adopting term martingale


stochastic process ref name hallheyde page ref ref name dynkin ref methods theory martingales became popular solving various probability problems techniques theory developed study markov processes applied martingales conversely methods theory martingales established treat markov processes ref name meyer fields probability developed used study stochastic processes one main approach theory large deviations ref name meyer theory many applications statistical physics among fields core ideas going back least later fundamental work


done alexander wentzell soviet union monroe donsker srinivasa varadhan united states america ref name ellis page ref would later result varadhan winning abel prize ref name raussenskau ref theories schramm loewner evolution ref name henkelkarevski page ref rough paths ref name frizvictoir page ref introduced developed study stochastic processes mathematical objects probability theory respectively resulted fields medals awarded wendelin werner ref name werner fields ref martin hairer ref name hairer fields ref theory stochastic processes still continues focus research


yearly international conferences topic stochastic processes ref name blathimkeller ref name applebaum page discoveries specific stochastic processes although khinchin gave mathematical definitions stochastic processes ref name doob ref name vere jones page specific stochastic processes already discovered different settings brownian motion process poisson process ref name jarrowprotter ref name guttorpthorarinsdottir families stochastic processes point processes renewal processes long complex histories stretching back centuries ref name daleyvere jones chap ref bernoulli process bernoulli process serve mathematical model flipping biased coin possibly first stochastic process studied ref name florescu page


process sequence independent bernoulli trials ref name bertsekastsitsiklis page named jackob bernoulli used study games chance including probability problems proposed studied earlier christiaan huygens ref name hald page ref bernoulli 's work including bernoulli process published book ''ars conjectandi'' ref name lebowitz ref random walks karl pearson coined term ''random walk'' posing problem describing random walk plane motivated application biology problems involving random walks already studied fields certain gambling problems studied


centuries earlier considered problems involving random walks ref name weiss page ref name lebowitz example problem known ''gambler 's ruin'' based simple random walk ref name karlintaylor page ref name florescu page ref example random walk absorbing barriers ref name seneta page ref name ibe page ref pascal fermat huyens gave numerical solutions problem without detailing methods ref name hald page ref detailed solutions presented jakob bernoulli abraham de moivre ref name hald page ref random walks math n math dimensional integer lattices george p lya published work studied probability symmetric random walk returning


previous position lattice p lya showed symmetric random walk equal probability advance direction lattice return previous position lattice infinite number times probability one one two dimensions probability zero three higher dimensions ref name florescu page ref ref name hughes page ref wiener process wiener process brownian motion process origins different fields including statistics finance physics ref name jarrowprotter thorvald thiele wrote paper method least squares used process


study errors model time series analysis ref name thiele ref ref name hald page ref ref name lauritzen page ref work considered early discovery statistical method known kalman filtering work largely overlooked thought ideas thiele 's paper advanced understood broader mathematical statistical community time ref name lauritzen page norbert wiener gave first mathematical proof existence wiener process mathematical object appeared previously work thorvald thiele louis bachelier albert einstein ref name jarrowprotter french mathematician louis bachelier used


wiener process thesis ref name bachelier ref ref name bachelier b ref order model price changes paris bourse stock exchange ref name courtaultkabanov ref without knowing work thiele ref name jarrowprotter speculated bachelier drew ideas random walk model jules regnault bachelier cite ref name jovanovic ref bachelier 's thesis considered pioneering field financial mathematics ref name courtaultkabanov ref name jovanovic commonly thought bachelier 's work gained little attention forgotten decades rediscovered leonard savage become popular


liquids using ideas kinetic theory gases einstein derived differential equation known diffusion equation describing probability finding particle certain region space shortly einstein 's first paper brownian movement marian smoluchowski published work cited einstein wrote independently derived equivalent results using different method ref name brush page ref einstein 's work well experimental results obtained jean perrin later inspired norbert wiener ref name brush page ref use type measure theory developed percy daniell fourier analysis


prove existence wiener process mathematical object ref name jarrowprotter poisson process poisson process named sim poisson due definition involving poisson distribution poisson never studied process ref name stirzaker ref name daleyvere jones page ref number claims early uses discoveries poisson process ref name stirzaker ref name guttorpthorarinsdottir beginning th century poisson process would arise independently different situations ref name stirzaker ref name guttorpthorarinsdottir sweden filip lundberg published thesis containing work considered fundamental pioneering proposed model insurance claims homogeneous poisson process ref


name embrechtsfrey page ref ref name cram r ref another discovery occurred denmark ak erlang derived poisson distribution developing mathematical model number incoming phone calls finite time interval erlang time aware poisson 's earlier work assumed number phone calls arriving interval time independent found limiting case effectively recasting poisson distribution limit binomial distribution ref name stirzaker ernest rutherford hans geiger published experimental results counting alpha particles motivated


extension independent random sequences ref name first paper markov chains published markov showed certain conditions average outcomes markov chain would converge fixed vector values proving weak law large numbers without independence assumption ref name ref ref name grinsteadsnell page ref ref name bremaud pageix ref ref name hayes ref commonly regarded requirement mathematical laws hold ref name hayes markov later used markov chains study distribution vowels eugene onegin written alexander pushkin proved central limit theorem chains ref name ref name grinsteadsnell page


poincar studied markov chains finite groups aim study card shuffling early uses markov chains include diffusion model introduced paul tatyana ehrenfest branching process introduced francis galton henry william watson preceding work markov ref name grinsteadsnell page ref name bremaud pageix work galton watson later revealed branching process independently discovered studied around three decades earlier ir n e jules bienaym ref name seneta ref starting maurice fr chet became interested markov chains eventually resulting publishing


detailed study markov chains ref name grinsteadsnell page ref name bruhertz ref andrei kolmogorov developed paper large part early theory continuous time markov processes ref name cramer ref name kendallbatchelor page kolmogorov partly inspired louis bachelier 's work fluctuations stock market well norbert wiener 's work einstein 's model brownian movement ref name kendallbatchelor page ref name barbutlocker page ref introduced studied particular set markov processes known diffusion processes derived set differential equations describing processes ref name kendallbatchelor page ref name skorokhod page ref independent kolmogorov 's work sydney chapman derived paper equation called


chapman kolmogorov equation less mathematically rigorous way kolmogorov studying brownian movement ref name bernstein ref differential equations called kolmogorov equations ref name anderson pagevii ref kolmogorov chapman equations ref name kendallbatchelor page ref mathematicians contributed significantly foundations markov processes include william feller starting later eugene dynkin starting ref name cramer l vy processes l vy processes wiener process poisson process real line named paul l vy started studying ref name applebaum page connections infinitely divisible distributions going back


ref name bertoin pageviii paper kolmogorov derived characteristic function random variables associated l vy processes result later derived general conditions l vy khinchin independently gave alternative form characteristic function ref name cramer ref name applebaumbook page ref addition l vy khinchin kolomogrov early fundamental contributions theory l vy processes made bruno de finetti kiyosi ref name bertoin pageviii mathematical construction mathematics constructions mathematical objects needed also case stochastic processes prove exist mathematically ref name rosenthal page


two main approaches constructing stochastic process one approach involves considering measurable space functions defining suitable measurable mapping probability space measurable space functions deriving corresponding finite dimensional distributions ref name adler page ref another approach involves defining collection random variables specific finite dimensional distributions using kolmogorov 's existence theorem ref kolmogorov 's extension theorem ref name ksendal page ref daniell kolmogorov theorem ref name williams page ref prove corresponding stochastic process exists ref name rosenthal page ref name adler page theorem existence theorem measures infinite product spaces ref name durrett page ref says finite dimensional distributions


satisfy two conditions known ''consistency conditions'' exists stochastic process finite dimensional distributions ref name rosenthal page construction issues constructing continuous time stochastic processes certain mathematical difficulties arise due uncountable index sets occur discrete time processes ref name kloedenplaten page ref name khoshnevisan page one problem possible one stochastic process finite dimensional distributions example left continuous modification right continuous modification poisson process finite dimensional distributions ref name billingsley page ref means distribution stochastic process necessarily specify uniquely properties


sample functions stochastic process ref name adler page ref name borovkov page ref another problem functionals continuous time process rely upon uncountable number points index set may measurable probabilities certain events may well defined ref name ito page example supremum stochastic process random field necessarily well defined random variable ref name adlertaylor page ref name khoshnevisan page continuous time stochastic process math x math characteristics depend uncountable number points index set math math include ref name ito page sample function stochastic process math x math continuous function


points index set ref name adlertaylor page ref furthermore stochastic process separable functionals uncountable number points index set measurable probabilities studied ref name ito page ref name adlertaylor page another approach possible originally developed anatoliy skorokhod andrei kolmogorov ref name athreyalahiri page ref continuous time stochastic process metric space state space construction stochastic process assumed sample functions stochastic process belong suitable function space usually skorokhod space consisting right continuous functions left limits


notes references reading articles books external links stochastic models statistical data types


'''determinism''' philosophical view events determined completely previously existing causes deterministic theories throughout history philosophy sprung diverse sometimes overlapping motives considerations opposite determinism kind indeterminism otherwise called nondeterminism randomness determinism often contrasted free although philosophers claim two compatible ref name franklin example see ref determinism often taken mean ''causal determinism'' physics known cause effect concept events within given paradigm bound causality way

Humanities Philosophy Metaphysics Determinism


state object event completely determined prior states meaning distinguished varieties determinism mentioned debates often concern scope determined systems maintaining entire universe single determinate system others identifying limited determinate systems multiverse numerous historical debates involve many philosophical positions varieties determinism include debates concerning determinism free technically denoted compatibilistic allowing two coexist incompatibilistic denying coexistence possibility determinism confused self determination


human actions reasons motives desires determinism interactions affect cognitive processes life cause result done life cause result always bounded together cognitive processes assumes observer sufficient information object human observer might able predict every consequent move object human determinism rarely requires perfect prediction practically possible varieties determinism may commonly refer following viewpoints


deliberating choosing acting certain way blockquote causal determinism proposes unbroken chain prior occurrences stretching back origin universe relation events may specified origin universe causal determinists believe nothing universe uncaused self caused causal determinism also considered generally idea everything happens exists caused antecedent conditions ref name stanfordincompatibilism http platostanfordedu entries incompatibilism arguments arguments incompatibilism stanford encyclopedia philosophy ref case nomological determinism conditions considered events also implying


future determined completely preceding events combination prior states universe laws nature ref name sepcausaldeterminism yet also considered metaphysical origin case theological determinism ref name sepmoralresponsibility many philosophical theories determinism frame idea reality follows sort predetermined path nomological nomological determinism generally synonymous physical determinism opposite physical indeterminism common form causal determinism notion past present dictate future entirely necessarily rigid natural laws


every occurrence results inevitably prior events nomological determinism sometimes illustrated thought experiment laplace 's demon ref name laplace laplace posited omniscient observer knowing infinite precision positions velocities every particle universe could predict future entirely discussion see another view determinism discussed ref nomological determinism sometimes called ' 'scientific determinism'' although misnomer necessitarianism necessitarianism closely related causal determinism described metaphysical principle denies mere possibility exactly one way


world leucippus claimed uncaused events everything occurs reason necessity predeterminism predeterminism idea events determined advance ref name mckewan ref concept often argued invoking causal determinism implying unbroken chain prior occurrences stretching back origin universe case predeterminism chain events pre established human actions cannot interfere outcomes pre established chain predeterminism used mean pre established causal determinism case


determinism ref name sepdeterminism http platostanfordedu entries determinism causal sep causal determinism ref form teleological determinism fatalism idea everything fated happen humans control future fate arbitrary power need follow causal otherwise deterministic laws ref name stanfordincompatibilism types fatalism include hard theological determinism idea predestination god determines humans may accomplished either knowing actions advance via form omniscience ref name fischer fischer john martin ''god foreknowledge freedom'' stanford california stanford university press


ref decreeing actions advance ref name watt watt montgomery ''free predestination early islam'' london luzac co ref theological determinism theological determinism form determinism holds events happen either preordained ie predestined happen monotheistic deity destined occur given omniscience two forms theological determinism exist referred ' 'strong'' ''weak'' theological determinism ref name jordantate ref strong theological determinism based concept creator deity dictating events history everything happens predestined happen


omniscient omnipotent divinity ref name iannone ref weak theological determinism based concept divine foreknowledge god 's omniscience perfect god knows future inevitably happen means consequently future already fixed ref name huyssteen ref exist slight variations categorisation however claim either theological determinism requires predestination events outcomes divinity ie classify weaker version ''theological determinism'' unless libertarian free assumed denied consequence weaker version constitute ''theological determinism'' ref name vanarragon ref respect free


theological determinism thesis god exists infallible knowledge true propositions including propositions future actions minimal criteria designed encapsulate forms theological determinism ref name stanfordincompatibilismarguments ref theological determinism also seen form causal determinism antecedent conditions nature god ref name sepmoralresponsibility asserted augustine hippo introduced theological determinism christianity ce whereas prior christian authors supported free stoic gnostic determinism however many biblical passages seem support


idea kind theological determinism logical determinism fact even without full understanding microscopic physics predict distribution coin tosseslogical determinism ' 'determinateness'' notion propositions whether past present future either true false note one support causal determinism without necessarily supporting logical determinism vice versa depending one 's views nature time also randomness problem free especially salient logical determinism choices free given propositions


future already truth value present referred problem future contingents often synonymous logical determinism ideas behind spatio temporal determinism eternalism view special relativity j j c smart proponent view uses term ''tenselessness'' describe simultaneous existence past present future physics block universe hermann minkowski albert einstein assumes time fourth dimension like three spatial dimensions adequate determinism adequate determinism idea quantum decoherence quantum indeterminacy


accepts linear causal sets sequential events adequate consistency yet also suggests constant forking causal chains creating multiple universes account multiple outcomes single events meaning causal set events leading present valid yet appear singular linear time stream within much broader unseen conic probability field outcomes split locally observed timeline model causal sets still consistent yet exclusive singular iterated outcomes interpretation side steps exclusive retrospective causal chain problem could


done otherwise suggesting outcome exist set parallel universe time streams split action occurred theory sometimes described example agent based choices involved models argue recursive causal splitting occurs particle wave functions play model highly contested multiple objections scientific community philosophical varieties determinism nature nurture controversy nature nurture interact humans scientist looking sculpture time ask whether seeing effects starting materials


environmental influences although forms determinism concern human behaviors cognition others frame answer debate nature nurture suggest one factor entirely determine behavior scientific understanding grown however strongest versions theories widely rejected single cause fallacy ref name melo martin ref words modern deterministic theories attempt explain interaction nature ''and'' nurture entirely predictable concept heritability helpful making distinction biological determinism sometimes called ''genetic determinism''


idea human behaviors beliefs desires fixed human genetic nature behaviorism involves idea behavior traced specific causes either environmental reflexive john b watson b f skinner developed nurture focused determinism cultural determinism along social determinism nurture focused theory culture raised determines cultural materialism contends physical world impacts sets constraints human behavior environmental determinism also known ''climatic'' ''geographical determinism'' proposes physical environment rather social conditions determines culture supporters


one factor would allow us make perfect predictions psychological determinism mean humans must act according reason also synonymous sort psychological egoism latter view humans always act according perceived best interest linguistic determinism claims language determines least limits things think say thus know sapir whorf hypothesis argues individuals experience world based grammatical structures habitually use economic determinism attributes primacy economic structure politics development human


history associated dialectical materialism karl marx technological determinism reductionist theory presumes society 's technology drives development social structure cultural values structural determinism structural determinism philosophical view actions events processes predicated determined structural factors given particular structure set estimable components concept emphasises rational predictable outcomes chilean biologists humberto maturana francisco varela popularised notion writing living system 's general order maintained via circular process ongoing self referral


thus organisation structure defines changes undergoes according authors system undergo changes state alteration structure without loss identity disintegrations alteration structure loss identity changes disintegrations ascertained elements disturbing agent disturbance trigger responses respective system turn determined system structure individualistic level means human beings free independent entities triggered react external stimuli change circumstance however


conceptualised writings karl marx within context structural determinism well example louis althusser structural marxist argues state political economic legal structures reproduces discourse capitalism turn allowing burgeoning capitalistic structures proponents notion highlight usefulness structural determinism study complicated issues related race gender highlights often gilded structural conditions block meaningful change critics call rigid reductionist inflexible additionally also criticise notion overemphasising deterministic forces structure role


hold free might exist hard determinists determinism hold free exist dutch philosopher baruch spinoza determinist thinker argued human freedom achieved knowledge causes determine desire affections defined human servitude state bondage anyone aware desires ignorant causes determined however free virtuous person becomes capable reason knowledge genuinely free even determined dutch philosopher


acting one 's internal necessity genuine freedom driven exterior determinations akin bondage spinoza 's thoughts human servitude liberty respectively detailed fourth fifth volumes work ''ethics'' standard argument free according philosopher j j c smart focuses implications determinism free suggests free denied whether determinism true determinism true actions predicted one assumed free however determinism false actions presumed


random one seems free part controlling happens soul determinists argue materialism present complete understanding universe describe determinate interactions among material things ignores minds souls conscious beings number positions delineated immaterial souls exist idealism immaterial souls exist exert non deterministic causal influence bodies traditional free interactionist dualism immaterial souls exist part deterministic framework immaterial souls exist exert


causal influence free determined epiphenomenalism occasionalism immaterial souls exist mind body dichotomy materialistic explanation intuitions contrary ethics morality another topic debate implication determinism morality hard determinism particularly criticized seeming make traditional moral judgments impossible philosophers find acceptable conclusion philosopher incompatibilist peter van inwagen introduces thesis arguments free required moral judgments moral judgment ''x'' done implies something


heraclitus leucippus later aristotle mainly stoics main philosophers dealt issue marcus aurelius omar khayy thomas hobbes baruch spinoza gottfried leibniz david hume baron d'holbach paul heinrich dietrich pierre simon laplace arthur schopenhauer william james friedrich nietzsche albert einstein niels bohr ralph waldo emerson recently john searle ted honderich daniel dennett mecca chiesa notes probabilistic selectionistic determinism b f skinner comprised wholly separate conception determinism mechanistic mechanistic determinism assumes every event unbroken chain


prior occurrences selectionistic probabilistic model western tradition west elements determinism expressed greece th century bce presocratics heraclitus leucippus first full fledged notion determinism appears originate stoics part theory universal causal determinism resulting philosophical debates involved confluence elements aristotelian ethics stoic psychology led st rd centuries ce works alexander aphrodisias first recorded western debate determinism freedom issue


known theology paradox free writings epictetus well middle platonist early christian thought instrumental development jewish philosopher moses maimonides said deterministic implications omniscient god god know know certain individual good bad thou sayest 'he knows' necessarily follows man compelled act god knew beforehand would act otherwise god 's knowledge would imperfect ref name maimonides ''the eight chapters maimonides ethics semonah perakhim '' edited annotated translated


introduction joseph gorfinkle pp new york ams press ref newtonian mechanics determinism west often associated newtonian mechanics physics depicts physical matter universe operating according set fixed knowable laws billiard ball hypothesis product newtonian physics argues initial conditions universe established rest history universe follows inevitably actually possible complete knowledge physical matter laws governing matter one time


would theoretically possible compute time place every event ever occur ''laplace 's demon'' sense basic particles universe operate fashion rolling balls billiard table moving striking predictable ways produce predictable results whether encompassing newtonian mechanics deals caused events example object begins known position hit dead object known velocity pushed straight toward


another predictable point goes somewhere else newtonians argue one must question one 's measurements original position object exact direction striking object gravitational fields inadvertently ignored etc maintain repeated experiments improvements accuracy always bring one 's observations closer theoretically predicted results dealing situations ordinary human scale newtonian physics enormously successful competition fails spectacularly velocities become substantial fraction speed light interactions


atomic scale studied discovery quantum effects challenges newtonian physics uncertainty always term applied accuracy human knowledge causes effects causes effects newtonian mechanics well following physical theories results observations experiments describe works within tolerance however old western scientists believed logical connections found observed cause effect must also absolute natural laws behind belief perfect natural laws driving


indian subcontinent concept ''karma'' deals similar philosophical issues western concept determinism karma understood spiritual mechanism causes entire cycle rebirth ie ''sa ra'' karma either positive negative accumulates according individual 's actions throughout life death determines nature next life cycle sa ra major religions originating india hold belief degree notably hinduism jainism sikhism buddhism views interaction karma free numerous diverge


greatly example sikhism god 's grace gained worship erase one 's karmic debts belief reconciles principle karma monotheistic god one must freely choose worship jainists believe sort compatibilism cycle sa sara completely mechanistic process occurring without divine intervention jains hold atomic view reality particles karma form fundamental microscopic building material universe buddhism buddhist philosophy contains several concepts scholars describe deterministic various levels however direct analysis


buddhist metaphysics lens determinism difficult due differences european buddhist traditions thought one concept argued support hard determinism idea dependent origination claims phenomena ' 'dharma'' necessarily caused phenomenon said ' 'dependent'' like links massive chain traditional buddhist philosophy concept used explain functioning cycle ' 'sa ra'' actions exert karmic force manifest results future lives words righteous unrighteous


actions one life necessarily cause good bad responses another another buddhist concept many scholars perceive deterministic idea non self ''anatta'' ref name buddhism attaining enlightenment involves one realizing humans fundamental core called soul humans instead made several constantly changing factors bind cycle sa ra ref name buddhism website encyclopedia britannica language en access date ref scholars argue concept non self necessarily disproves ideas free moral culpability autonomous


self view events necessarily unchangeably caused others type autonomy said exist moral otherwise however scholars disagree claiming buddhist conception universe allows form compatibilism buddhism perceives reality occurring two different levels ultimate reality truly understood enlightened illusory false material reality therefore buddhism perceives free notion belonging material reality concepts like non self dependent origination belong ultimate reality transition


two truly understood buddhists claim one attained enlightenment modern scientific perspective generative processes although thought scientists indeterminism quantum mechanics occurred small scale influence biological neurological systems indication nervous systems influenced quantum indeterminism due chaos theory unclear implications problem free given various possible reactions problem first place many biologists grant determinism christof koch instance argues


free experienced due generation infinite behaviour interaction finite deterministic set rules parameters thus unpredictability emerging behaviour deterministic processes leads perception free even though free ontological entity exist ref name kenrick ref name nowak ref name axtell ref name epstein conway 's game life interaction four simple rules creates patterns seem somehow alive illustration strategy board games chess go rigorous rules information cards' face values hidden either


player random events dice rolling happen within game yet chess especially go extremely simple deterministic rules still extremely large number unpredictable moves chess simplified fewer pieces however endgame tables available dictate moves play achieve perfect game implies given less complex environment original pieces reduced fewer pieces perfectly predictable game chess possible scenario winning player announce checkmate happen


within given number moves assuming perfect defense losing player fewer moves defending player chooses sub optimal moves game progresses inevitable predicted conclusion analogy suggested experience free emerges interaction finite rules deterministic parameters generate nearly infinite practically unpredictable behavioural responses theory events could accounted known way evaluate events seemingly unpredictable behaviour would become predictable ref name kenrick ref name nowak ref name axtell ref name epstein another hands


example generative processes john horton conway 's playable game life nassim taleb wary models coined term ludic fallacy compatibility existence science certain philosophers science argue causal determinism everything including brain mind subject laws causality compatible minds capable science fatalism predestination philosophers make distinction causal determinism means step determined step therefore allows sensory input observational data determine conclusions brain reaches


physics extremely small revealed previously concealed aspects events newtonian physics physics everyday life dominated taken isolation rather approximation quantum mechanics newtonian physics depicts universe objects move perfectly determined ways scale humans exist interact universe newtonian mechanics remain useful make relatively accurate predictions eg calculating trajectory bullet whereas theory absolute knowledge forces accelerating bullet would produce absolutely accurate prediction path modern quantum mechanics casts reasonable doubt main


thesis determinism quantum realm quantum physics works differently many ways newtonian physics physicist aaron o'connell explains understanding universe small scales atoms requires different logic day day life o'connell deny interconnected scale human existence ultimately emerge quantum scale o'connell argues must simply use different models constructs dealing quantum world quantum mechanics product careful application scientific method logic empiricism heisenberg uncertainty principle frequently confused


observer effect uncertainty principle actually describes precisely may measure position momentum particle time increase accuracy measuring one quantity forced lose accuracy measuring uncertainty relations give us measure freedom limitations classical concepts necessary consistent description atomic processes ref name heisenberg ref although possible predict trajectory one particle obey determined probabilities permit prediction statistical mechanics come play


physicists begin require rather unintuitive mental models particle 's path simply cannot exactly specified full quantum description path classical practical attribute everyday life one quantum particles meaningfully possess probabilities discovered quantum mechanics nevertheless arise measurement perceived path particle stephen hawking explains result traditional determinism rather determined probabilities ref name gdesign grand design p molecular basis biology shows biological processes governed laws physics chemistry therefore


determined orbits planetsso seems biological machines free illusion p quantum physics might seem undermine idea nature governed laws case instead leads us accept new form determinism given state system time laws nature determine probabilities various futures pasts rather determining future past certainty discussing many worlds interpretation ref cases quantum particle


may indeed trace exact path probability finding particles path one certain true fact far prediction goes quantum development least predictable classical motion key describes wave functions cannot easily expressed ordinary language far thesis determinism concerned probabilities least quite determined findings quantum mechanics found many applications allow us build transistors lasers put another way personal computers blu ray players


internet work humankind discovered determined probabilities quantum world ref name whatisitgoodfor http wwwscientificamericancom articlecfmid everyday quantum physics scientific american quantum mechanics good ref topic predictable probabilities double slit experiments popular example photons fired one one double slit apparatus distant screen arrive single point even two points lined slits way might expected bullets fired fixed gun distant target instead light arrives varying concentrations widely separated points distribution collisions


reconciled without giving determinism advanced variations arguments include quantum contextuality bell simon b kochen ernst specker argues hidden variable theories cannot sensible meaning values hidden variables inherently depend devices used measure debate relevant possibly specific situations arrival electron screen certain point time would trigger one event whereas arrival another point would trigger entirely different event eg see schr dinger 's cat


thought experiment used part deeper debate thus quantum physics casts reasonable doubt traditional determinism classical newtonian physics far reality seem absolutely determined subject famous bohr einstein debates einstein niels bohr still consensus adequate determinism see varieties reason stephen hawking calls libertarian free illusion ref name gdesign see also ''amor fati'' calvinism digital physics false necessity fractal game theory ilya prigogine interpretations quantum mechanics laplace 's demon lazy reason ''notes


underground'' open theism philosophical interpretation classical physics positivism radical behaviorism superdeterminism voluntarism wheeler feynman absorber theory references notes bibliography daniel dennett ''freedom evolves'' viking penguin john earman aspects determinism modern physics butterfield j earman j eds ''philosophy physics part b'' north holland george ellis physics real world ''physics today'' epstein jm axtell r ''growing artificial societies social science bottom'' mit press harris james ''of liberty necessity free debate eighteenth century british philosophy'' clarendon press albert messiah ''quantum mechanics''


history ideas'' http wwwuclacuk uctytho dfwintroindexhtm philosopher ted honderich 's determinism web resource http wwwinformationphilosophercom freedom determinismhtml determinism information philosopher http wwwdeterminismcom society natural science http wwwchabadorg articleaspaid determinism free judaism http wwwjottingsca john cogitationshtml snooker pool determinism https wwwthefactssitecom life game game lifehtml game life life game play philosophy science metaphysical theories randomness causality


process creating writing new piece music people create new compositions called composers composers primarily songs usually called songwriters songs person writes lyrics song lyricist many cultures including western classical music act composing typically includes creation music notation sheet music score performed composer musicians popular music traditional music songwriting may involve creation basic outline song called lead sheet sets

Humanities
Performing arts
Music
Musical composition


melody lyrics chord progression classical music orchestration choosing instruments large music ensemble orchestra play different parts music melody accompaniment countermelody bassline typically done composer musical theatre pop music songwriters may hire arranger orchestration cases pop traditional songwriter may use written notation instead compose song mind play sing record memory jazz popular music notable


sound recordings influential performers given weight written printed scores play classical music although musical composition often uses musical notation single author always case work music multiple composers often occurs popular music members band collaborate write song musical theatre one person writes melodies second person writes lyrics third person orchestrates songs piece music also composed words images since th


century computer programs explain notate singer musician create musical sounds examples range th century avant garde music uses graphic notation text compositions karlheinz stockhausen 's ''aus den sieben tagen'' computer programs select sounds musical pieces music makes heavy use randomness chance called aleatoric music associated contemporary composers active th century john cage morton feldman witold lutos awski commonly known example chance based indeterminate music sound wind chimes jingling


popular song may exist recording music composed performed music performed memory norm instrumental soloists concerto performances singers opera shows art song recitals reading written musical notation norm large ensembles orchestras concert bands choirs combination methods example principal cello player orchestra may read accompaniment parts symphony playing tutti parts memorize exposed solo order able watch


conductor compositions comprise huge variety musical elements vary widely genres cultures popular music genres make extensive use electric electronic instruments electric guitar electric bass electric electronic instruments used contemporary classical music compositions concerts albeit lesser degree popular music music baroque music era example used acoustic mechanical instruments strings brass woodwinds timpani keyboard instruments harpsichord pipe organ era pop band may use electric guitar played


electronic effects guitar amplifier digital synthesizer keyboard electronic drums piece ''piece'' general non technical term began applied mainly instrumental compositions th century onwardsother taken individually 'piece' equivalents rarely used movements sonatas symphoniescomposers used terms different languages frequently compound forms eg klavierst ck vocal musicthe term frequently used operatic ensembles ref name grove tilmouth michael piece ''the new grove dictionary music musicians'' first edition vols edited stanley sadie vol


london macmillan publishers new york grove 's dictionaries ref musical form composition techniques draw parallels visual art 's formal elements sometimes entire form piece composed meaning part different repetition sections forms include strophic rondo verse chorus others pieces composed around set scale compositional technique might considered usage particular scale others composed performance see improvisation variety techniques also sometimes used used particular songs familiar


scale notes used including mode tonic note important tonal musical composition similarly music middle east employs compositions rigidly based specific mode maqam often within improvisational contexts indian classical music hindustani carnatic system indian tradition music tradition india many forms musical composition degree account many musical styles prevalent different regions country hindustani music carnatic music bengali music forth another


decide upon instrumentation original work contemporary composer virtually write almost combination instruments ranging string section wind brass sections used standard orchestras electronic instruments synthesizers common group settings include music full orchestra consisting strings woodwinds brass percussion concert band consists larger sections greater diversity woodwind brass percussion instruments usually found orchestra chamber group small number instruments least two composer may also choose


comment upon mash ups various contemporary classical works ref name baileyshea baileyshea matt http mtosocietymusictheoryorg issues mto mto baileysheahtml fn ref filleted mignon new recipe analysis recomposition ''music theory online'' volume number december ref interpretation even music notated relatively precisely western classical music onwards many decisions performer conductor make notation specify elements musical performance process deciding perform music previously composed notated termed interpretation different performers' conductor 's interpretations


work music vary widely terms tempos chosen playing singing style phrasing melodies composers songwriters present music concert interpreting songs much perform music others standard body choices techniques present given time given place referred performance practice whereas interpretation generally used mean individual choices performer copyright legal status copyright government granted monopoly


limited time gives composition 's owner composer composer 's employer case work hire set exclusive rights composition exclusive right publish sheet music describing composition performed copyright requires anyone else wanting use composition ways obtain license permission owner jurisdictions composer assign copyright part another party often composers n't business publishing companies temporarily assign copyright interests formal publishing companies


granting companies license control publication licensing composer 's work contract law copyright law governs composer publisher contracts ordinarily involve agreement profits publisher 's activities related work shared composer form royalties scope copyright general defined various international treaties implementations take form national statutes common law jurisdictions case law agreements corresponding body law distinguish rights applicable sound recordings


rights applicable compositions example beethoven 's th symphony public domain world recordings particular performances composition usually copyright purposes song lyrics performed words considered part composition even though may different authors copyright owners non lyrical elements many jurisdictions allow compulsory licensing certain uses compositions example copyright law may allow record company pay modest fee copyright collective composer publisher belongs exchange right


make distribute cds containing cover band 's performance composer publisher 's compositions license compulsory copyright owner cannot refuse set terms license copyright collectives also typically manage licensing public performances compositions whether live musicians transmitting sound recordings radio internet us even though first us copyright laws include musical compositions added part copyright act according circular issued united states copyright office copyright registration


musical compositions sound recordings musical composition defined musical composition consists music including accompanying words normally registered work performing arts author musical composition generally composer lyricists musical composition may form notated copy example sheet music form phonorecord example cassette tape lp cd sending musical composition form phonorecord necessarily mean claim copyright


sound recording uk ''copyright designs patents act '' defines musical work mean work consisting music exclusive words action intended sung spoken performed music india india copy right act prevailed original literary dramatic musical artistic work copyright amendment act introduced amended act new definition provided musical work states musical works means work consisting music included graphical notation work


included words action intended sung spoken performed music ref name das ref see also bcm classification developing variation dickinson classification midi composition music manuscript music publisher popular music r pertoire international des sources musicales rism references sources reference laborde jean benjamin de ''essai sur la musique ancienne et moderne'' vols paris phd pierres eug ne onfroy reading siamo tutti compositori alcune riflessioni sulla distribuzione sociale del processo compositivo ''schweizer jahrbuch f r musikwissenschaft'' neue folge sorce keller marcello composition janet sturman


ed ''the sage encyclopedia music culture'' los angeles sage reference vol ii external links http wwwartofcomposingcom compose music compose music artofcomposingcom http wwwcompositiontodaycom composition today news competitions interviews resources composers https webarchiveorg web https wwwbsmnyorg icp ty internet concert project album young student new music online performance documentary feature http wwwbsmnyorg bloomingdale school music january https webarchiveorg web http wwwbsmnyorg exploring music features practical guides beginners guide composing beginner 's guide composing online feature http wwwbsmnyorg bloomingdale school music february http alanbelkinmusiccom bk indexhtml practical guide musical composition http wwwcomposersnewpencilcom composersnewpencil information articles music composition resources https webarchiveorg web http wwwlearn pianoorg compose musichtml


compose music http wwwwikihowcom compose music compose music wikihow http wwwrisminfo r pertoire international des sources musicales online database locations musical manuscripts around world http wwwquiescencemusiccom composemusichtml compose new age piano http wwwuremusiccom html composing music


amo studies atoms isolated system electrons atomic nucleus '''molecular physics''' study physical properties molecules term ''atomic physics'' often associated nuclear power nuclear bombs due synonymous use ''atomic'' ''nuclear'' standard english however physicists distinguish atomic physics deals atom system consisting nucleus electrons nuclear physics considers atomic nuclei alone important experimental techniques various types spectroscopy molecular physics closely related atomic physics

Natural science
Physics
Atomic, molecular, and optical physics


also overlaps greatly theoretical chemistry physical chemistry chemical physics subfields primarily concerned electronic structure dynamical processes arrangements change generally work involves using quantum mechanics molecular physics approach known quantum chemistry one important aspect molecular physics essential atomic orbital theory field atomic physics expands molecular orbital theory molecular physics concerned atomic processes molecules additionally concerned effects due molecular structure additionally electronic excitation states known


atoms molecules able rotate vibrate rotations vibrations quantized discrete energy levels smallest energy differences exist different rotational states therefore pure rotational spectra far infrared region wavelength electromagnetic spectrum vibrational spectra near infrared nbsp spectra resulting electronic transitions mostly visible ultraviolet regions measuring rotational vibrational spectra properties molecules like distance nuclei calculated many scientific fields strict delineation


highly contrived atomic physics often considered wider context ''atomic molecular optical physics'' physics research groups usually classified optical physics '''optical physics''' study generation electromagnetic radiation properties radiation interaction radiation matter especially manipulation control differs general optics optical engineering focused discovery application new phenomena strong distinction however optical physics applied optics optical engineering since devices optical


engineering applications applied optics necessary basic research optical physics research leads development new devices applications often people involved basic research applied technology development example experimental demonstration electromagnetically induced transparency e harris slow light harris lene vestergaard hau researchers optical physics use develop light sources span electromagnetic spectrum microwaves x rays field includes generation detection light linear nonlinear optical processes spectroscopy


lasers laser spectroscopy transformed optical science major study optical physics also devoted quantum optics coherence femtosecond optics ref name nap optical physics support also provided areas nonlinear response isolated atoms intense ultra short electromagnetic fields atom cavity interaction high fields quantum properties electromagnetic field important areas research include development novel optical techniques nano optical measurements diffractive optics low coherence interferometry optical coherence tomography near field microscopy research optical physics places emphasis ultrafast optical science


technology applications optical physics create advancements communications medicine manufacturing even entertainment history bohr model hydrogen atom one earliest steps towards ''atomic physics'' recognition matter composed ''atoms'' modern terms basic unit chemical element theory developed john dalton th century stage n't clear atoms although could described classified observable properties bulk summarized developing periodic table john newlands dmitri mendeleyev around mid


late th century ref name dickerson geis ref later connection atomic physics ''and'' optical physics became apparent discovery spectral lines attempts describe phenomenon notably joseph von fraunhofer fresnel others th century time physicists seeking explain atomic spectra blackbody radiation one attempt explain hydrogen spectral lines bohr atom model ref name dickerson geis experiments including electromagnetic radiation matter photoelectric effect compton effect spectra sunlight due unknown


element helium limitation bohr model hydrogen numerous reasons lead entirely new mathematical model matter light quantum mechanics classical oscillator model matter early models explain origin index refraction treated electron atomic system classically according model paul drude hendrik lorentz theory developed attempt provide origin wavelength dependent refractive index ''n'' material model incident electromagnetic waves forced electron bound atom oscillate amplitude


oscillation would relationship frequency incident electromagnetic wave resonant frequencies oscillator superposition emitted waves many oscillators would lead wave moved slowly ref name haken ref early quantum model matter light max planck derived formula describe electromagnetic field inside box thermal equilibrium ref name haken model consisted superposition standing waves one dimension box length ''l'' sinusoidal waves wavenumber math k frac n pi l math occur


box ''n'' positive integer mathematically denoted math scriptstyle n mathbb n math equation describing standing waves given math e e sin left frac n pi l x right math ''e'' sub sub magnitude electric field amplitude ''e'' magnitude electric field position ''x'' basic planck 's law derived ref name haken ernest rutherford concluded based alpha particle scattering atom central pointlike proton also thought electron would still attracted proton coulomb 's law verified still held small


albert einstein photoelectric effect led association light wave frequency math nu math photon energy math h nu math einstein created extension bohrs model introduction three processes stimulated emission spontaneous emission absorption electromagnetic radiation ref name haken modern treatments largest steps towards modern treatment formulation quantum mechanics matrix mechanics approach werner heisenberg discovery schr dinger equation erwin schr dinger ref name haken variety semi classical treatments within amo aspects


dynamics electrons described semi classical initial conditions calculated using fully quantum treatment treatment classical ref name drake isolated atoms molecules atomic molecular optical physics frequently considers atoms molecules isolation atomic models consist single nucleus may surrounded one bound electrons whilst molecular models typically concerned molecular hydrogen molecular hydrogen ion concerned processes ionization threshold ionization excitation photons collisions atomic particles modelling atoms


isolation may seem realistic one considers molecules gas plasma time scales molecule molecule interactions huge comparison atomic molecular processes concerned means individual molecules treated isolation vast majority time consideration atomic molecular physics provides underlying theory plasma physics atmospheric physics even though deal huge numbers molecules electronic configuration electrons form notional shells around nucleus naturally ground


state excited absorption energy light photons magnetic fields interaction colliding particle typically electrons electrons populate shell said bound state energy necessary remove electron shell taking infinity called binding energy quantity energy absorbed electron excess amount converted kinetic energy according conservation energy atom said undergone process ionization event electron


absorbs quantity energy less binding energy may transition excited state virtual state statistically sufficient quantity time electron excited state undergo transition lower state via spontaneous emission change energy two energy levels must accounted conservation energy neutral atom system emit photon difference energy however lower state inner shell phenomenon known auger effect may take place


energy transferred another bound electrons causing go continuum allows one multiply ionize atom single photon strict selection rules electronic configurations reached excitation light however rules excitation collision processes see also born oppenheimer approximation frequency doubling diffraction hyperfine structure interferometry isomeric shift metamaterial cloaking molecular energy state molecular modeling nanotechnology negative index metamaterials nonlinear optics optical engineering photon polarization quantum chemistry quantum optics rigid rotor spectroscopy superlens stationary state transition state vector model


atom notes references ''solid state physics nd edition '' jr hook hall manchester physics series john wiley sons ''light matter electromagnetism optics spectroscopy lasers'' yb band john wiley sons ''the light fantastic introduction classic quantum optics'' ir kenyon oxford university press ''handbook atomic molecular optical physics'' editor gordon drake springer various authors external links http wwwsciencedirectcom science bookseries x sciencedirect advances atomic molecular optical physics http iopscienceioporg journal physics b atomic molecular optical physics institutions http wwwapsorg units damop american physical society division atomic


molecular optical physics https webarchiveorg web http ampdepsdivisionsorg european physical society atomic molecular optical physics division https wwwnsfgov funding pgm summjsppims id national science foundation atomic molecular optical physics http cuawebmitedu mit harvard center ultracold atoms https webarchiveorg web http jilacoloradoedu research atomic molecular physics atomic molecular physics jila atomic molecular physics http jqiumdedu joint quantum institute university maryland nist http wwwphyornlgov ornl physics division http webamqubacuk ctamop queen 's university belfast center theoretical atomic molecular optical physics http physicsberkeleyedu research atomic molecular optical physics university california berkeley atomic molecular optical physics


pathology may also refer predicted actual progression particular diseases statement many different forms cancer diverse pathologies case proper choice word would pathophysiologies affix ''pathy'' sometimes used indicate state disease cases physical ailment cardiomyopathy psychological conditions psychopathy physician practicing pathology called ''pathologist'' field general inquiry research pathology addresses components disease cause mechanisms development pathogenesis structural alterations cells morphologic changes


consequences changes clinical manifestations common medical practice general pathology mostly concerned analyzing known clinical abnormalities markers precursors infectious non infectious disease conducted experts one two major specialties anatomical pathology clinical pathology divisions specialty exist basis involved sample types comparing example cytopathology hematopathology histopathology organs renal pathology physiological systems oral pathology well basis focus examination forensic pathology pathology significant field


name long ref hellenic period ancient greece concerted causal study disease underway see medicine ancient greece many notable early physicians hippocrates modern hippocratic oath named developed methods diagnosis prognosis number diseases medical practices romans byzantines continued greek roots many areas scientific inquiry growth understanding medicine stagnated classical era continued slowly develop throughout numerous cultures notably many advances made


medieval era islam see medicine medieval islam numerous texts complex pathologies developed also based greek tradition even growth complex understanding disease mostly languished knowledge experimentation began proliferate renaissance enlightenment baroque eras following resurgence empirical method new centers scholarship th century study rudimentary microscopy underway examination tissues led british royal society member robert hooke coin word cell setting stage later germ theory modern pathology began


multiplication replacing earlier beliefs humors even spiritual agents dominated much previous years european medicine new understanding causative agents physicians began compare characteristics one germ 's symptoms developed within affected individual another germ 's characteristics symptoms approach led foundational understanding diseases able replicate many profound varied effects human host determine causes diseases medical experts used common widely accepted assumptions symptoms


times general principal approach persists modern medicine modern medicine particularly advanced developments microscope analyze tissues rudolf virchow gave significant contribution leading slew research developments late early pathology deemed medical specialty combined developments understanding general physiology beginning th century study pathology begun split number distinct fields resulting development large number modern specialties within pathology related disciplines


medical school secure license practice medicine structurally study disease divided many different fields study diagnose markers disease using methods technologies particular specific scales organs tissue types information section mostly concerns pathology regards common medical practice systems specialties also subject voluminous pathology research regards disease pathways specific pathogens disorders affect tissues discrete organs structures see also gross pathology anatomical pathology anatomical pathology ''commonwealth'' anatomic


pathology ''united states'' medical specialty concerned diagnosis disease based gross microscopic chemical immunologic molecular examination organs tissues whole bodies general examination autopsy anatomical pathology divided subfields main divisions surgical pathology cytopathology forensic pathology anatomical pathology one two main divisions medical practice pathology clinical pathology diagnosis disease laboratory analysis bodily fluids tissues sometimes pathologists practice anatomical clinical pathology combination known


general pathology cytopathology bone marrow smear case erythroleukemia large cell top center abnormal erythroblast multinucleated megaloblastoid nuclear chromatin diagnostic erythroleukemia cytopathology sometimes referred cytology branch pathology studies diagnoses diseases cellular level usually used aid diagnosis cancer also helps diagnosis certain infectious diseases inflammatory conditions well thyroid lesions diseases involving sterile body cavities peritoneal pleural cerebrospinal wide range


body sites cytopathology generally used samples free cells tissue fragments contrast histopathology studies whole tissues cytopathologic tests sometimes called smear tests samples may smeared across glass microscope slide subsequent staining microscopic examination however cytology samples may prepared ways including cytocentrifugation dermatopathology malignant melanoma often suspected sight confirmation diagnosis outright removal requires excisional biopsy dermatopathology subspecialty anatomic pathology focuses skin rest


able recognize skin diseases based appearances anatomic distributions behavior sometimes however criteria lead conclusive diagnosis skin biopsy taken examined microscope using usual histological tests cases additional specialized testing needs performed biopsies including immunofluorescence immunohistochemistry electron microscopy flow cytometry molecular pathologic analysis one greatest challenges dermatopathology scope different disorders skin exist including cutaneous eruptions rashes neoplasms therefore dermatopathologists must maintain broad base knowledge clinical


dermatology familiar several specialty areas medicine forensic pathology pathologist performing human dissection abdominal thoracic organs autopsy room forensic pathology focuses determining cause death post mortem examination corpse partial remains autopsy typically performed coroner medical examiner often criminal investigations role coroners medical examiners also frequently asked confirm identity corpse requirements becoming licensed practitioner forensic pathology varies country country even within given


nation typically minimal requirement medical doctorate specialty general anatomical pathology subsequent study forensic medicine methods forensic scientists use determine death include examination tissue specimens identify presence absence natural disease microscopic findings interpretations toxicology body tissues fluids determine chemical cause overdoses poisonings cases involving toxic agents examinations physical trauma forensic pathology major component trans disciplinary field forensic science histopathology instance diagnosis via histopathology


body organism placed fixative stabilizes tissues prevent decay common fixative formalin although frozen section fixing also common see tissue microscope sections stained one pigments aim staining reveal cellular components counterstains used provide contrast histochemistry refers science using chemical reactions laboratory chemicals components within tissue histological slides interpreted diagnostically resulting pathology report describes histological findings opinion


pathologist case cancer represents tissue diagnosis required treatment protocols neuropathology coronal cross section brain reveals significant arteriovenous malformation occupies much parietal lobe neuropathology study disease nervous system tissue usually form either surgical biopsies sometimes whole brains case autopsy neuropathology subspecialty anatomic pathology neurology neurosurgery many english speaking countries neuropathology considered subfield anatomical pathology physician specializes neuropathology usually completing fellowship


residency anatomical general pathology called neuropathologist day day clinical practice neuropathologist consultant physicians disease nervous system suspected diagnosis cannot made less invasive methods biopsy nervous tissue taken brain spinal cord aid diagnosis biopsy usually requested mass detected medical imaging autopsies principal work neuropathologist help post mortem diagnosis various conditions affect central nervous system biopsies


also consist skin epidermal nerve fiber density testing enfd recently developed neuropathology test punch skin biopsy taken identify small fiber neuropathies analyzing nerve fibers skin test becoming available select labs well many universities replaces traditional nerve biopsy test less invasive pulmonary pathology pulmonary pathology subspecialty anatomic especially surgical pathology deals diagnosis characterization neoplastic non neoplastic diseases lungs thoracic pleura diagnostic specimens often obtained via bronchoscopic transbronchial


biopsy ct guided percutaneous biopsy video assisted thoracic surgery tests necessary diagnose infection inflammation fibrotic conditions renal pathology tissue cross section demonstrates gross pathology polycystic kidneys renal pathology subspecialty anatomic pathology deals diagnosis characterization disease kidneys medical setting renal pathologists work closely nephrologists transplant surgeons typically obtain diagnostic specimens via percutaneous renal biopsy renal pathologist must synthesize findings traditional microscope histology electron microscopy immunofluorescence obtain definitive diagnosis medical renal diseases may affect


surgically removed patient determinations usually accomplished combination gross ie macroscopic histologic ie microscopic examination tissue may involve evaluations molecular properties tissue immunohistochemistry laboratory tests two major types specimens submitted surgical pathology analysis biopsies surgical resections biopsy small piece tissue removed primarily surgical pathology analysis often order render definitive diagnosis types biopsies include core biopsies obtained use large bore needles sometimes


guidance radiological techniques ultrasound ct scan magnetic resonance imaging incisional biopsies obtained diagnostic surgical procedures remove part suspicious lesion whereas excisional biopsies remove entire lesion similar therapeutic surgical resections excisional biopsies skin lesions gastrointestinal polyps common pathologist 's interpretation biopsy critical establishing diagnosis benign malignant tumor differentiate different types grades cancer well determining activity specific molecular pathways tumor surgical resection specimens


obtained therapeutic surgical removal entire diseased area organ occasionally multiple organs procedures often intended definitive surgical treatment disease diagnosis already known strongly suspected pathological analysis specimens remains important confirming previous diagnosis clinical pathology clinical pathology medical specialty concerned diagnosis disease based laboratory analysis bodily fluids blood urine well tissues using tools chemistry clinical microbiology hematology molecular pathology clinical pathologists work


close collaboration medical technologists hospital administrations referring physicians clinical pathologists learn administer number visual microscopic tests especially large variety tests biophysical properties tissue samples involving automated analysers cultures sometimes general term laboratory medicine specialist used refer working clinical pathology including medical doctors phds doctors pharmacology immunopathology study organism 's immune response infection sometimes considered fall within domain clinical pathology ref name bulletin ref hematopathology clinical chemistry automated blood chemistry analyzer hematopathology


study diseases blood cells including constituents white blood cells red blood cells platelets tissues organs comprising hematopoietic system term hematopoietic system refers tissues organs produce primarily host hematopoietic cells includes bone marrow lymph nodes thymus spleen lymphoid tissues united states hematopathology board certified subspecialty licensed american board pathology practiced physicians completed general pathology residency anatomic clinical combined additional year fellowship training hematology


hematopathologist reviews biopsies lymph nodes bone marrows tissues involved infiltrate cells hematopoietic system addition hematopathologist may charge flow cytometric molecular hematopathology studies molecular pathology molecular pathology focused upon study diagnosis disease examination molecules within organs tissues bodily fluids molecular pathology multidisciplinary nature shares aspects practice anatomic pathology clinical pathology molecular biology biochemistry proteomics genetics often applied context much scientific


directly medical encompasses development molecular genetic approaches diagnosis classification human diseases design validation predictive biomarkers treatment response disease progression susceptibility individuals different genetic constitution particular disorders crossover molecular pathology epidemiology represented related field molecular pathological epidemiology molecular pathology commonly used diagnosis cancer infectious diseases molecular pathology primarily used detect cancers melanoma brainstem glioma brain tumors well many types cancer infectious diseases techniques


numerous include quantitative polymerase chain reaction qpcr multiplex pcr dna microarray situ hybridization dna sequencing antibody based immunofluorescence tissue assays molecular profiling pathogens analysis bacterial genes antimicrobial resistance ref name cai ref techniques used based analyzing samples dna rna pathology widely used gene therapy disease diagnosis oral maxillofacial pathology many conditions case geographic tongue diagnosed partly gross examination may confirmed tissue pathology oral maxillofacial pathology one nine dental specialties recognized american dental association


pathologist generally requires specialty training medical school individual nations vary medical licensing required pathologists united states pathologists physicians md completed four year undergraduate program four years medical school training three four years postgraduate training form pathology residency training may within two primary specialties recognized american board pathology anatomical pathology clinical pathology requires separate board certification american osteopathic board pathology also recognizes four primary specialties anatomic pathology dermatopathology forensic