a note on the markov property of stochastic processes described by nonlinear fokker planck equations abstract we study the markov property of processes described by generalized fokker planck equations that are nonlinear with respect to probability densities such as mean field fokker planck equations and fokker planck equations related to generalized thermostatistics we show that their transient solutions describe non markov processes in contrast stationary solutions can describe markov processes as a result nonlinear fokker planck equations can be used to model transient non markov processes that converge to stationary markov processes

deviations from universality in the fluctuation behavior of a heterogeneous complex system reveal intrinsic properties of components the case of the international currency market abstract identifying behavior that is relatively invariant under different conditions is a challenging task in far from equilibrium complex systems as an example of how the existence of a semi invariant signature can be masked by the heterogeneity in the properties of the components comprising such systems we consider the exchange rate dynamics in the international currency market we show that the exponents characterizing the heavy tails of fluctuation distributions for different currencies systematically diverge from a putative universal form associated with the median value 2 of the exponents we relate the degree of deviation of a particular currency from such an inverse square law to fundamental macroscopic properties of the corresponding economy viz measures of per capita production output and diversity of export products we also show that in contrast to uncorrelated random walks exhibited by the exchange rate dynamics for currencies belonging to developed economies those of the less developed economies show characteristics of sub diffusive processes which we relate to the anti correlated nature of the corresponding fluctuations approaches similar to that presented here may help in identifying invariant features obscured by the heterogeneous nature of components in other complex systems

correlation measure to detect time series distances whence economy globalization abstract an instantaneous time series distance is defined through the equal time correlation coefficient the idea is applied to the gross domestic product gdp yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation some data discussion is first presented to decide what eks gk or derived gdp series should be studied distances are then calculated from the correlation coefficient values between pairs of series the role of time averaging of the distances over finite size windows is discussed three network structures are next constructed based on the hierarchy of distances it is shown that the mean distance between the most developed countries on several networks actually decreases in time which we consider as a proof of globalization an empirical law is found for the evolution after 1990 similar to that found in flux creep the optimal observation time window size is found 15 years

polynomial realization of the uq sl 3 gel fand weyl zetlin basis an explicit realization of the u uq sl 3 gel fand weyl zetlin gwz basis as polynomial functions in three variables real or complex is given this realization is obtained in two complementary ways first a known correspondence is used between the abstract gwz basis and explicit polynomials in the quantum subgroup u of the raising generators then an explicit construction is used of arbitrary lowest weight holomorphic representations of u in terms of three variables on which the generators of u are realized as q difference operators the application of the gwz corresponding polynomials in this realization of the lowest weight vector the function 1 produces the first realization of this gwz basis another realization of the gwz polynomial basis is found by the explicit diagonalization of the operators of isospin i2 third component of isospin iz and hypercharge in the same realization as q difference operators the result is that the eigenvectors can be written in terms of q hypergeometric

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

self similarity and network perspective of the chinese fund market abstract by testing 88 different funds of the chinese fund market cfm we find fractal behavior and long range correlations in the return series which are insensitive to the kind of funds meanwhile a power law relationship between the deviation d of prices and the hurst exponent h has been obtained which may be useful for predicting the price time series in addition with funds being viewed as nodes and the connections among the funds being determined by the cross correlation coefficients using a winner takes all approach we investigate the topological properties of the fund network our analysis reveals that during different time periods the cumulative degree distributions of the fund network all obey the double power law format moreover the small world property is also found for the fund network

a q analog of the gauss summation theorem for hypergeometric series in u n in this paper we derive a q analog of holman s u n generalization of the gauss summation theorem this result is obtained by iterating our mutivariable generalization of the gauss reduction formula for basic hypergeometric series in u n multiple series generalizations of both classical q analogs of the vandermonde summation theorem appear as special cases we obtain the corresponding theorems for ordinary series by taking the limit as q 1 of all these results

percolation critical exponents in scale free networks we study the behavior of scale free networks having connectivity distribution p k k 2l close to the percolation threshold we show that for networks with 3 l 4 known to undergo a transition at a finite threshold of dilution the critical exponents are different than the expected mean field values of regular percolation in infinite dimensions networks with 2 l 3 possess only a percolative phase nevertheless we show that in this case percolation critical exponents are well defined near the limit of extreme dilution where all sites are removed and that also then the exponents bear a strong l dependence the regular mean field values are recovered only for l 4

representation theory approach to the polynomial solutions of q difference equations uq sl 3 and beyond a new approach to the theory of polynomial solutions of q difference equations is proposed the approach is based on the representation theory of simple lie algebras g and their q deformations and is presented here for uq sl n first a q difference realization of uq sl n in terms of n n 1 2 commuting variables and depending on n 1 complex representation parameters ri is constructed from this realization lowest weight modules lwm are obtained which are studied in detail for the case n 3 the well known n 2 case is also recovered all reducible lwm are found and the polynomial bases of their invariant irreducible subrepresentations are explicitly given this also gives a classification of the quasi exactly solvable operators in the present setting the invariant subspaces are obtained as solutions of certain invariant q difference equations i e these are kernels of invariant q difference operators which are also explicitly given such operators were not used until now in the theory of polynom

reducing stochasticity in the north atlantic oscillation index with coupled langevin equations we present a critical investigation of the functional relationship between the two pressure time series routinely used to define the index characterizing the north atlantic oscillation nao well known to regulate global climate variability and change first by a standard markov analysis we show that the standard nao index based on the pressure difference is not optimal in the sense of producing sufficiently reliable forecasts because it contains a dominating stochastic term in the corresponding langevin equation then we introduce a variationally optimized markov analysis involving two coupled langevin equations tailored to produce a nao quasi index having the desired minimum possible stochasticity the variationally optimized markov analysis is very general and can be applied in other physical situations involving two or more time series

dynamical stochastic processes of returns in financial markets abstract we study the evolution of probability distribution functions of returns from the tick data of the korean treasury bond ktb futures and the s p 500 stock index which can be described by means of the fokker planck equation we show that the fokker planck equation and the langevin equation from the estimated kramers moyal coefficients can be estimated directly from the empirical data by analyzing the statistics of the returns we present quantitatively the deterministic and random influences on financial time series for both markets for which we can give a simple physical interpretation we particularly focus on the diffusion coefficient which may be important for the creation of a portfolio

exact time dependence of solutions to the time dependent schrodinger equation solutions of the schrodinger equation with an exact time dependence are derived as eigenfunctions of dynamical invariants which are constructed from time independent operators using time dependent unitary transformations exact solutions and a closed form expression for the corresponding time evolution operator are found for a wide range of time dependent hamiltonians in d dimensions including non hermitean symmetric hamiltonians hamiltonians are constructed using time dependent unitary spatial transformations comprising dilatations translations and rotations and solutions are found in several forms as eigenfunctions of a quadratic invariant as coherent state eigenfunctions of boson operators as plane wave solutions from which the general solution is obtained as an integral transform by means of the fourier transform and as distributional solutions for which the initial wavefunction is the dirac function for the isotropic harmonic oscillator in d dimensions radial solutions are found which extend known results for d 1 including barut girardello and perelomov coherent states i e vector coherent states which are shown to be related to eigenfunctions of the quadratic invariant by the transformation this transformation which leaves the ermakov equation invariant implements su 1 1 transformations on linear dynamical invariants coherent states are derived also for the time dependent linear potential exact solutions are found for hamiltonians with electromagnetic interactions in which the time dependent magnetic and electric fields are not necessarily spatially uniform as an example it is shown how to find exact solutions of the time dependent schrodinger equation for the dirac magnetic monopole in the presence of time dependent magnetic and electric fields of a specified form

can log periodic power law structures arise from random fluctuations abstract recent research has established log periodic power law lppl patterns prior to the detonation of the german stock index dax bubble in 1998 the purpose of this article is to explore whether a langevin equation extracted from real world data can generate synthetic time series with comparable lppl structures to this end we first estimate the stochastic process underlying the dax log returns during the period from mid 1997 until end 2003 the employed data set contains about 3 93 10 6 intraday dax quotes at a sampling rate of 15 s our results indicate that the dax log returns can be described as a markov process as a consequence a langevin equation is derived based on this model equation we run extensive simulations in order to generate 100 synthetic dax trajectories each covering 3000 trading days we find lppl behavior in ten artificial time series moreover we can establish a link between lppl patterns and ensuing bubble bursts in seven synthetic 600 week windows however the lppl components in most synthetic trajectories differ fundamentally from those lppl structures that have previously been detected in real financial time series summarized this paper demonstrates that lppl structures are not necessarily the signature of imitative behavior among investors but can also stem from noise even though the likelihood of this is extremely low thus our findings confirm with high statistical confidence that the lppl structures in the dax development are rooted deeper than only in the random fluctuations of the german stock market

langevin equations from time series we discuss the link between the approach to obtain the drift and diffusion of one dimensional langevin equations from time series and pope and ching s relationship for stationary signals the two approaches are based on different interpretations of conditional averages of the time derivatives of the time series at given levels the analysis provides a useful indication for the correct application of pope and ching s relationship to obtain stochastic differential equations from time series and shows its validity in a generalized sense for nondifferentiable processes originating from langevin equations

correlation effects in a discrete quantum random walk we introduce memory dependent discrete time quantum random walk models by adding uncorrelated memory terms and also by modifying the hamiltonian of the walker to include couplings with memory keeping agents we next study numerically the correlation effects in these models we also propose a correlation exponent as a relevant and promising tool for investigation of correlation or memory hence non markovian effects our analysis can easily be applied to more realistic models in which different regimes may emerge because of competition between different underlying physical mechanisms

representations of uh su n derived from quantum flag manifolds a relationship between quantum flag and grassmann manifolds is revealed this enables a formal diagonalization of quantum positive matrices the requirement that this diagonalization defines a homomorphism leads to a left uh su n module structure on the algebra generated by quantum antiholomorphic coordinate functions living on the flag manifold the module is defined by prescribing the action on the unit and then extending it to all polynomials using a quantum version of the leibniz rule the leibniz rule is shown to be induced by the dressing transformation for discrete values of parameters occurring in the diagonalization one can extract finite dimensional irreducible representations of uh su n as cyclic submodules

coherent state theory of the noncompact symplectic group an extended coherent state theory is presented for the noncompact sp 3 r group which reveals a simple relationship between the sp 3 r algebra and its contracted u 3 boson limit the relationship is used to derive a remarkably accurate analytic expression for sp 3 r matrix elements for the generic lowest weight representations the expression is shown to be exact whenever the states involved are multiplicity free with respect to the u 3 subalgebra it is further shown how exact matrix elements are easily calculated in general dyson and holstein primakoff type u 3 boson expansions are given

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

inverse statistics and information content abstract inverse statistics analysis studies the distribution of investment horizons to achieve a predefined level of return this distribution provides a maximum investment horizon which determines the most likely horizon for gaining a specific return there exists a significant difference between inverse statistics of financial market data and a fractional brownian motion fbm as an uncorrelated time series which is a suitable criteria to measure information content in financial data in this paper we perform this analysis for the djia and s p500 as two developed markets and tehran price index tepix as an emerging market we also compare these probability distributions with fbm probability to detect when the behavior of the stocks are the same as fbm

clustering of volatility in variable diffusion processes abstract increments in financial markets have anomalous statistical properties including fat tailed distributions and volatility clustering i e the autocorrelation functions of return increments decay quickly but those of the squared increments decay slowly one of the central questions in financial market analysis is whether the nature of the underlying stochastic process can be deduced from these statistical properties we have shown previously that a class of variable diffusion processes has fat tailed distributions here we show analytically that such models also exhibit volatility clustering to our knowledge this is the first case where clustering of volatility is proven analytically in a model our results are compatible with the viewpoint that variable diffusion processes are possible models for financial markets

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

left regular representation of slq 3 reduction and intertwiners reduction of the left regular representation of the quantum algebra slq 3 is studied and q difference intertwining operators are constructed the irreducible representations correspond to a q deformation of the spaces of local sections of certain line bundles over the flag manifold

a theory of fluctuations in stock prices abstract the distribution of price returns is studied for a class of market models with markovian dynamics the models have a non constant diffusion coefficient that depends on the value of the return an analytical expression for the distribution of returns is obtained and shown to match the results of computer simulations for two simple cases those two cases are shown to have exponential and fat tailed power law decaying distributions respectively

implementation of the u n tensor operator calculus in a vector bargmann hilbert space using a vector coherent state framework and an associated vector bargmann hilbert space 1961 the structure of two classes of u n u n 1 unit projective operators is shown to be intimately related to 6 j and 9 j coefficients of the u n 1 subalgebra explicit verification of limit properties for these operators allows the unambiguous assignment of a set of canonical operator labels

the first 20 min in the hong kong stock market based on the minute by minute data of the hang seng index in hong kong and the analysis of probability distribution and autocorrelations we nd that the index uctuations for the rst few minutes of daily opening show behaviors very dierent from those of the other times in particular the properties of tail distribution which will show the power law scaling with exponent about four or an exponential type decay the volatility and its correlations depend on the opening eect of each trading day c 2000 elsevier science b v all rights reserved

stochastic order parameter equation of isometric force production revealed by drift diffusion estimates we address two questions that are central to understanding human motor control variability what kind of dynamical components contribute to motor control variability i e deterministic and or random ones and how are those components structured to this end we derive a stochastic order parameter equation for isometric force production from experimental data using drift diffusion estimates we show that the force variability increases with the required force output because of a decrease of deterministic stability and an accompanying increase of noise intensity a structural analysis reveals that the deterministic component consists of a linear control loop while the random component involves a noise source that scales with force output in addition we present evidence for the existence of a subject independent overall noise level of human isometric force production

application of the beck model to stock markets value at risk and portfolio risk assessment abstract we apply the beck model developed for turbulent systems that exhibit scaling properties to stock markets our study reveals that the beck model elucidates the properties of stock market returns and is applicable to practical use such as the value at risk estimation and the portfolio analysis we perform empirical analysis with daily intraday data of the s p500 index return and find that the volatility fluctuation of real markets is well consistent with the assumptions of the beck model the volatility fluctuates at a much larger time scale than the return itself and the inverse of variance or inverse temperature obeys distribution as predicted by the beck model the distribution of returns is well fitted by q gaussian distribution of tsallis statistics the evaluation method of value at risk var one of the most significant indicators in risk management is studied for q gaussian distribution our proposed method enables the var evaluation in consideration of tail risk which is underestimated by the variance covariance method a framework of portfolio risk assessment under the existence of tail risk is considered we propose a multi asset model with a single volatility fluctuation shared by all assets named the single model and empirically examine the agreement between the model and an imaginary portfolio with dow jones indices it turns out that the single model gives good approximation to portfolios composed of the assets with non gaussian and correlated returns

on the piano movers problem i the case of a two dimensional rigid polygonal body moving amidst polygonal barriers we present an algorithm that solves a two dimensional case of the following problem which arises in robotics given a body b and a region bounded by a collection of walls either find a continuous motion connecting two given positions and orientations of b during which b avoids collision with the walls or else establish that no such motion exists the algorithm is polynomial in the number of walls o n5 if n is the number of walls but for typical wall configurations can run more efficiently it is somewhat related to a technique outlined by reif

how to quantify deterministic and random influences on the statistics of the foreign exchange market it is shown that price changes of the u s dollar german mark exchange rates upon different delay times can be regarded as a stochastic marcovian process furthermore we show how kramers moyal coefficients can be estimated from the empirical data finally we present an explicit fokker planck equation which models very precisely the empirical probability distributions in particular their non gaussian heavy tails

fokker planck equation of distributions of financial returns and power laws abstract our purpose is to relate the fokker planck formalism proposed by friedrich et al phys rev lett 84 2000 5224 for the distribution of stock market returns to the empirically well established power law distribution with an exponent in the range 3 5 we show how to use friedrich et al s formalism to predict that the distribution of returns is indeed asymptotically a power law with an exponent that can be determined from the kramers moyal coefficients determined by friedrich et al however with their values determined for the u s dollar german mark exchange rates the exponent predicted from their theory is found to be around 12 in disagreement with the often quoted value between 3 and 5 this could be explained by the fact that the large asymptotic value of 12 does not apply to real data that lie still far from the stationary state of the fokker planck description another possibility is that power laws are inadequate the mechanism for the power law is based on the presence of multiplicative noise across time scales which is different from the multiplicative noise at fixed time scales implicit in the arch models developed in the finance literature

closed form solutions for the levy stable distribution the levy stable distribution is the attractor of distributions which hold power laws with infinite variance this distribution has been used in a variety of research areas for example in economics it is used to model financial market fluctuations and in statistical mechanics it is used as a numerical solution of fractional kinetic equations of anomalous transport this function does not have an explicit expression and no uniform solution has been proposed yet this paper presents a uniform analytical approximation for the levy stable distribution based on matching power series expansions for this solution the trans stable function is defined as an auxiliary function which removes the numerical issues of the calculations of the levy stable distribution then the uniform solution is proposed as a result of an asymptotic matching between two types of approximations called the inner solution and the outer solution finally the results of analytical approximation are compared to the numerical results of the levy stable distribution function making this uniform solution valid to be applied as an analytical approximation

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

stochastic nature of series of waiting times although fluctuations in the waiting time series have been studied for a long time some important issues such as its long range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied here we find that the waiting times series for a given increment level have long range correlations with hurst exponents belonging to the interval 1 2lhl1 we also study positive negative level asymmetry of the waiting time distribution we find that the logarithmic difference of waiting times series has a short range correlation and then we study its stochastic nature using the markovian method and determine the corresponding kramers moyal coefficients as an example we analyze the velocity fluctuations in high reynolds number turbulence and determine the level dependence of markov time scales as well as the drift and diffusion coefficients we show that the waiting time distributions exhibit power law tails and we were able to model the distribution with a continuous time random walk

variable step random walks and self similar distributions we study a scenario under which variable step random walks give anomalous statistics we begin by analyzing the martingale central limit theorem to find a sufficient condition for the limit distribution to be non gaussian we study the case when the scaling index is 12 for corresponding continuous time processes it is shown that the probability density function w x t satisfies the fokker planck equation possible forms for the diffusion coefficient are given and related to w x t finally we show how a time series can be used to distinguish between these variable diffusion processes and levy dynamics

a class of fokker planck equations with logarithmic factors in diffusion and drift terms the x2 ln x dependence of the diffusion coefficient in the fokker planck equation is retrieved by means of symmetry arguments exact solutions of the equation with logarithmic factors in coefficients are presented algebraic and log algebraic solutions are found for some values of exponents they seem to be analogues on an interval of log normal distributions

analysis of price diffusion in financial markets using puck model based on the new type of random walk process called the potentials of unbalanced complex kinetics puck model we theoretically show that the price diffusion in large scales is amplified 2 2 b 1 times where b is the coefficient of quadratic term of the potential in short time scales the price diffusion depends on the size m of the super moving average both numerical simulations and real data analysis of yen dollar rates are consistent with theoretical analysis r 2007 elsevier b v all rights reserved

induced module construction for highest weight representations of uq gl n at roots of unity a method is investigated for inducing highest weight representations for the quantum group uq gl n from the canonical subalgebra uq gl n 1 when q is a root of unity we classify the irreps into two types typical and atypical where the former is a generalization of the class of irreps with maximal dimensionality the structures of both the typical and atypical irreps are studied in particular a sufficiency condition is given for an irrep to be typical as examples we consider flat representations induced from a one dimensional representation of the canonical subalgebra and representations induced from vector representation

improved estimation of fokker planck equations through optimization an improved method for the description of hierarchical complex systems by means of a fokker planck equation is presented in particular the limited memory broyden fletcher goldfarb shanno algorithm for constraint problems is used to minimize the distance between the numerical solutions of the fokker planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the fokker planck equation the optimization routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this optimization routine

vector coherent state realization of representations of the affine superalgebra a 1 0 1 the method of vector coherent states is generalized to study the representations of the affine superalgebra a 1 0 1 a new realization of all the irreducible highest weight representations of this affine superalgebra is obtained in terms of holomorphic superdifferential operators in infinitely many grassmannian and bosonic variables

estimation of drift and diffusion functions from time series data a maximum likelihood framework complex systems are characterized by a huge number of degrees of freedom often interacting in a nonlinear manner in many cases macroscopic states however can be characterized by a small number of order parameters that obey stochastic dynamics in time recently techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced this paper develops a framework for the estimation of the functions and their respective bayesian posterior confidence regions based on likelihood estimators in succession approximations are introduced that significantly improve the efficiency of the estimation procedure while being consistent with standard approaches to the problem this paper solves important problems concerning the applicability and the accuracy of estimated parameters

efficient motion planning for an l shaped object an algorithm that solves the following motion planning problem is presented given an l shaped body l and a two dimensional region with n point obstacles decide whether there is a continuous motion connecting two given positions and orientations of l during which l avoids collision with the obstacles the algorithm requires o n 2 log 2 n time and o n 2 storage the algorithm is a variant of the cell decomposition technique of the configuration space d leven and m sharir j algorithms 8 1987 pp 192 215 j t schwartz and m sharir comm pure appl math 36 1983 pp 345 398 but it employs a new and efficient technique for obtaining a compact representation of the free space which results in a saving of nearly an order of magnitude the approach used in our algorithm is also applicable to motion planning of certain robotic arms whose spaces of free placements have a structure similar to that of the l shaped body

normalized uq sl 3 gel fand weyl zetlin basis and new summation formulas for q hypergeometric functions an explicit realization of the normalized gel fand weyl zetlin gwz basis for uq sl 3 in terms of polynomial functions in three variables real or complex is given the construction uses two different realizations of the uq sl 3 unnormalized gwz basis which were given previously and whose transformation properties were not known it turns out that finding these properties enables us to find the gwz dependent proportionality constant between these two realizations the scalar product is also fixed by this in both unnormalized realizations and then by normalization the normalized gwz states are obtained as by products new summation formulas are obtained which seem new also for q 1 the main new formula is a double sum which is given in terms of the proportionality constant mentioned above this double sum can be written as single sum over a q 3f2 hypergeometric function or as a q hypergeometric function of two variables

an extension of the borel weil construction to the quantum group u q n the borel weil bw construction for unitary irreps of a compact lie group is extended to a construction of all unitary irreps of the quantum groupu q n thisq bw construction uses a recursion procedure foru q n in which the fiber of the bundle carries an irrep ofu q n 1 u q 1 with sections that are holomorphic functions in the homogeneous spaceu q n u q n 1 u q 1 explicit results are obtained for theu q n irreps and for the related isomorphism of quantum group algebras

from brownian motion to operational risk statistical physics and financial markets abstract high frequency returns of the dax german blue chip stock index are used to test geometric brownian motion the standard model for financial time series even on a 15 s time scale the linear correlations of dax returns have a zero time delta function which carries 90 of the weight while the remaining 10 are positively correlated with a decay time of 53 s and negatively correlated on a 9 4 min scale the probability density of the returns possesses fat tails with power laws whose exponents continuously increase with time scales it is suggested that hydrodynamic turbulence may provide a phenomenological framework for the description of these data and at the same time open a way to use them for risk management purposes e g option pricing and hedging option pricing also is the cornerstone of credit valuation an area of much practical importance not considered explicitly in most other physics inspired papers on finance finally operational risk is introduced as a new risk category currently emphasized by regulators which will become important in many banks in the near future

darboux transformations for 1 2 dimensional fokker planck equations with constant diffusion matrix we construct a darboux transformation for 1 2 dimensional fokker planck equations with constant diffusion matrix our transformation is based on the two dimensional supersymmetry formalism for the schrodinger equation the transformed fokker planck equation and its solutions are obtained in explicit form

self organized criticality in a network of economic agents with finite consumption abstract we introduce a minimal agent model to explain the emergence of heavy tailed return distributions as a result of self organized criticality the model assumes that agents trade their economic outputs with each other composing a complex network of agents and connections further the incoming degree of an agent is proportional to the demand on its goods while its outgoing degree is proportional to the supply the model considers a collection of economic agents which are attracted to establish connections among them to make an exchange at a price formed by supply and demand with our model we are able to reproduce the evolution of the return of macroscopic quantities indices and to correctly retrieve the non trivial exponent value characterizing the amplitude of drops in several indices in financial markets relating it to the underlying topology of connections the distribution of drops in empirical data is obtained by counting the number of successive time steps for which a decrease in the index value is observed all eight financial indexes show an exponent m 5 2 finally we present mean field calculations of the critical exponents and of the scaling relation m 3 2 1 between the exponent m for the distribution of drops and the topological exponent for the degree distribution

log amplitude statistics of intermittent and non gaussian time series in studies of hydrodynamic turbulence and nonequilibrium systems it has been demonstrated that the observed non gaussian probability density functions are often described effectively by a superposition of gaussian distributions with fluctuating variances based on this framework we propose a general method to characterize intermittent and non gaussian time series in our approach an observed time series is assumed to be described by the multiplication of gaussian and amplitude random variables where the amplitude variable describes the variance fluctuation it is shown analytically that statistical properties of the log amplitude fluctuations can be estimated using the logarithmic absolute moments of the observed time series this method is applicable to a wide variety of symmetric unimodal distributions with heavy tails in order to quantify the deviation from a gaussian distribution by analyzing random cascade type processes and superstatistical non gaussian models with power law tails we demonstrate that our method can provide detailed characterization in a wide range of non gaussian fluctuations

averaged time evolution of rough surfaces we propose a method of extracting an approximated evolution equation of distribution of height fluctuations for a class of discrete growth models of rough surfaces where the behavior of local slopes can be described by a markov process using the markov property of the fluctuating field the evolution equation is obtained as a map describing the time evolution averaged over possible growth paths applying the method to a dimensional restricted solid on solid model we obtain a map with finite degrees of freedom the obtained map describes well the averaged evolution of surfaces

on the q oscillator and the quantum algebra suq 1 1 the authors discuss some problems of the q deformed harmonic oscillator different q bosonisations of the quantum suq 1 1 algebra are given and the corresponding infinite dimensional representations of discrete series are analysed

predicting foreign currency exchange rates using the numerical solution of the incompressible navier stokes equations abstract the movement of exchange rates has similarities with physical phenomena especially the movement of fluid in turbulence the parameters change of the data information on the foreign exchange market will result in unstable exchange rates movement these are according to changes in energy in the turbulence flow resulting in fluid particles moving randomly at fluctuating velocity this study will predict the exchange rates of the united states dollar usd to indonesian rupiah idr using the incompressible navier stokes equations which have been modified with economic parameters the analogy of economic parameters to physical parameters such as gross domestic product gdp as the distance between the two measured velocity points the trade balance of two countries as fluid viscosity and fluid flow velocity as exchange rate changes while the inflation rates and interest rates are external forces the numerical solution of the navier stokes equations is solved using the crank nicolson finite difference method the results of the prediction of the exchange rate of usd to idr are compared with actual exchange rate data the exchange rate prediction results of the navier stokes equations that calculated using the crank nicolson scheme for one year produce an error percentage below 2 5 of the actual exchange rate data

a langevin equation for the rates of currency exchange based on the markov analysis we propose a method for analyzing the data for the rates of exchange of various currencies versus the u s dollar the method analyzes the return time series of the data as a markov process and develops an effective equation which reconstructs it we find that the markov time scale i e the time scale over which the data are markov correlated is one day for the majority of the daily exchange rates that we analyze we derive an effective langevin equation to describe the fluctuations in the rates the equation contains two quantities d 1 and d 2 representing the drift and diffusion coefficients respectively we demonstrate how the two coefficients are estimated directly from the data without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the u s dollar r 2007 elsevier b v all rights reserved

computing a face in an arrangement of line segments and related problems this paper presents a randomized incremental algorithm for computing a single face in an arrangement of n line segments in the plane that is fairly simple to implement the expected running time of the algorithm is o n alpha n log n the analysis of the algorithm uses a novel approach that generalizes and extends the clarkson shor analysis technique in discrete comput geom 4 1989 pp 387 421 a few extensions of the technique obtaining efficient randomized incremental algorithms for constructing the entire arrangement of a collection of line segments and for computing a single face in an arrangement of jordan arcs are also presented

movement problems for 2 dimensional linkages this paper is motivated by questions concerning the planning of motion in robotics in particular it is concerned with the motion of planar linkages from the complexity point of view there are two main results first a planar linkage can be constrained to stay inside a bounded region whose boundary consists of straight lines by the addition of a polynomial number of new links second the question of whether a planar linkage in some initial configuration can be moved so that a designated joint reaches a given point in the plane is pspace hard

coherent states for quantum compact groups coherent states are introduced and their properties are discussed for simple quantum compact groupsal bl cl anddl the multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit the coherent state is interpreted as a holomorphic function on this orbit with values in the carrier hilbert space of an irreducible representation of the corresponding quantized enveloping algebra using gauss decomposition the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compactr matrix formulation generalizing this way theq deformed grassmann and flag manifolds the antiholomorphic realization of the irreducible representations of a compact quantum group the analogue of the borel weil construction is described using the concept of coherent state the relation between representation theory and non commutative differential geometry is suggested

evidence of markov properties of high frequency exchange rate data we present a stochastic analysis of a data set consisting of 106 quotes of the us dollar german mark exchange rate evidence is given that the price changes x upon different delay times can be described as a markov process evolving in thus the dependence of the probability density function pdf p x on the delay time can be described by a fokker planck equation a generalized diffusion equation for p x this equation is completely determined by two coefficients d1 x and d2 x drift and diffusion coefficient respectively we demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process furthermore it is shown that the solutions of the resulting fokker planck equation describe the empirical pdfs correctly including the pronounced tails

variable diffusion in stock market fluctuations abstract we analyze intraday fluctuations in several stock indices to investigate the underlying stochastic processes using techniques appropriate for processes with nonstationary increments the five most actively traded stocks each contains two time intervals during the day where the variance of increments can be fit by power law scaling in time the fluctuations in return within these intervals follow asymptotic bi exponential distributions the autocorrelation function for increments vanishes rapidly but decays slowly for absolute and squared increments based on these results we propose an intraday stochastic model with linear variable diffusion coefficient as a lowest order approximation to the real dynamics of financial markets and to test the effects of time averaging techniques typically used for financial time series analysis we find that our model replicates major stylized facts associated with empirical financial time series we also find that ensemble averaging techniques can be used to identify the underlying dynamics correctly whereas time averages fail in this task our work indicates that ensemble average approaches will yield new insight into the study of financial markets dynamics our proposed model also provides new insight into the modeling of financial markets dynamics in microscopic time scales

vector coherent state realization of representations of the affine lie algebra the method of vector coherent states is generalized to study representations of the affine lie algebra a large class of highest weight irreps is explicitly constructed which contains the integrable highest weight irreps as special cases

medium and small scale analysis of financial data abstract a stochastic analysis of financial data is presented in particular we investigate how the statistics of log returns change with different time delays the scale dependent behaviour of financial data can be divided into two regions the first time range the small timescale region in the range of seconds seems to be characterised by universal features the second time range the medium timescale range from several minutes upwards can be characterised by a cascade process which is given by a stochastic markov process in the scale a corresponding fokker planck equation can be extracted from given data and provides a non equilibrium thermodynamical description of the complexity of financial data

delay fokker planck equations perturbation theory and data analysis for nonlinear stochastic systems with time delays we study nonlinear stochastic systems with time delayed feedback using the concept of delay fokker planck equations introduced by guillouzic l heureux and longtin we derive an analytical expression for stationary distributions using first order perturbation theory we demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data in addition we show that the fokker planck perspective for stochastic systems with time delays is consistent with the so called extended phase space approach to time delayed systems

theoretical analysis of potential forces in markets abstract we show that random walks in a moving potential function with its center at the moving average of market prices are represented in the form of the self modulation model from this point of view we confirm the existence of non trivial autocorrelation in real market price changes by generalizing the formulation of potential function we prove that the arch model belongs to the special case of random walk in an asymmetric potential with randomly changing coefficient

a reactive lattice gas approach to economic cycles abstract a microscopic approach to macroeconomic features is intended a model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed a birth death lattice gas model taking into account the influence of an economic environment on the fitness and concentration evolution of economic entities is numerically and analytically examined the reaction diffusion model can also be mapped onto a high order logistic map the role of the selection pressure along various dynamics with entity diffusion on a square symmetry lattice has been studied by monte carlo simulation the model leads to a sort of phase transition for the fitness gap as a function of the selection pressure and to cycles the control parameter is a scalar business plan the business plan s allows for spin offs or merging and enterprise survival evolution law s whence bifurcations cycles and chaotic behavior