weak solutions of a class of quasilinear hyperbolic integro differential equations describing viscoelastic materials global weak solutions of scalar second order quasilinear hyperbolic integro differential equations with singular kernels are constructed perturbations of rest states are shown to propagate with finite speed smoothing effects of the solution operator are exhibited and conditions for the asymptotic stability of rest states are given the equations arise in viscoelasticity

scaling and memory in the non poisson process of limit order cancelation abstract the order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order driven markets we investigate the dynamics of order cancelation by studying the statistical properties of inter cancelation durations defined as the waiting times between consecutive order cancelations of 22 liquid stocks traded on the shenzhen stock exchange of china in year 2003 three types of cancelations are considered including cancelation of any limit orders of buy limit orders and of sell limit orders we find that the distributions of the inter cancelation durations of individual stocks can be well modeled by weibulls for each type of cancelation and the distributions of rescaled durations of each type of cancelations exhibit a scaling behavior for different stocks complex intra day patterns are also unveiled in the inter cancelation durations the detrended fluctuation analysis dfa and the multifractal dfa show that the inter cancelation durations possess long term memory and multifractal nature which are not influenced by the intra day patterns no clear crossover phenomenon is observed in the detrended fluctuation functions with respect to the time scale these findings indicate that the cancelation of limit orders is a non poisson process which has potential worth in the construction of order driven market models

complexity of normal form grammars abstract various types of grammars can be used to describe context free languages such are context free grammars and their normal form restrictions rewriting of a context free grammar to an equivalent grammar in required normal form can cause a change of parameters of the grammar such as the number of rules the number of nonterminals etc greibach normal form grammars and position restricted grammars will be investigated from the point of view of descriptional complexity of context free languages

identification of market trends with string and d2 brane maps abstract the multidimensional string objects are introduced as a new alternative for an application of string models for time series forecasting in trading on financial markets the objects are represented by open string with 2 endpoints and d2 brane which are continuous enhancement of 1 endpoint open string model we show how new object properties can change the statistics of the predictors which makes them the candidates for modeling a wide range of time series systems string angular momentum is proposed as another tool to analyze the stability of currency rates except the historical volatility to show the reliability of our approach with application of string models for time series forecasting we present the results of real demo simulations for four currency exchange pairs

generating all permutations by context free grammars in greibach normal form we consider context free grammars g n in greibach normal form and particularly in greibach m form m 1 2 which generates the finite language l n of all n strings that are permutations of n different symbols n 1 these grammars are investigated with respect to their descriptional complexity i e we determine the number of nonterminal symbols and the number of production rules of g n as functions of n as in the case of chomsky normal form these descriptional complexity measures grow faster than any polynomial function

scaling and memory in volatility return intervals in financial markets abstract for both stock and currency markets we study the return intervals between the daily volatilities of the price changes that are above a certain threshold q we find that the distribution function pq scales with the mean return interval as the scaling function f x is similar in form for all seven stocks and for all seven currency databases analyzed and f x is consistent with a power law form f x x with 2 we also quantify how the conditional distribution pq 0 depends on the previous return interval 0 and find that small or large return intervals are more likely to be followed by small or large return intervals this clustering of the volatility return intervals is a previously unrecognized phenomenon that we relate to the long term correlations known to be present in the volatility econophysics fluctuations extreme values long term correlations long term memory

cancellation in context free languages enrichment by reduction the following problem is shown to be decidable given a context free grammar g and a string w x does there exist a string u l g such that w is obtained from u by deleting all substrings ui that are elements of the symmetric dyck set d 1 the intersection of any two context free languages can be obtained from only one context free language by cancellation either with the smaller semi dyck set d 1 d 1 or with d 1 itself also the following is shown here for the first time if the set eq xnx n n n d 1 is used for this cancellation then each recursively enumerable set can be obtained from linear context free languages previous work has shown that cancellation of substrings from the semi dyck language d 1 or from any of the former languages d 1 or eq allows one to obtain the following from the context free languages any terminal petri net language 14 16 the intersections of any context free with a terminal petri net language and the nested iterated substitution thereof 15 we generalize this characterization by showing that linear context free languages suffice for generating terminal petri net languages in proving this we obtain a new closure property of the family of petri net languages which is not shared by the context free sets

relation between volatility correlations in financial markets and omori processes occurring on all scales we analyze the memory in volatility by studying volatility return intervals defined as the time between two consecutive fluctuations larger than a given threshold in time periods following stock market crashes such an aftercrash period is characterized by the omori law which describes the decay in the rate of aftershocks of a given size with time t by a power law with exponent close to 1 a shock followed by such a power law decay in the rate is here called omori process we find self similar features in the volatility specifically within the aftercrash period there are smaller shocks that themselves constitute omori processes on smaller scales similar to the omori process after the large crash we call these smaller shocks subcrashes which are followed by their own aftershocks we also show that the omori law holds not only after significant market crashes as shown by lillo and mantegna phys rev e 68 016119 2003 but also after intermediate shocks by appropriate detrending we remove the influence of the crashes and subcrashes from the data and find that this procedure significantly reduces the memory in the records moreover when studying long term correlated fractional brownian motion and autoregressive fractionally integrated moving average artificial models for volatilities we find omori type behavior after high volatilities thus our results support the hypothesis that the memory in the volatility is related to the omori processes present on different time scales

effect of nonlinear correlations on the statistics of return intervals in multifractal data sets we study the statistics of return intervals between events above a certain threshold in multifractal data sets without linear correlations we find that nonlinear correlations in the record lead to a power law i decay of the autocorrelation function of the return intervals ii increase in the conditional return period and iii decay in the probability density function of the return intervals we show explicitly that all the observed quantities depend both on the threshold value and system size and hence there is no simple scaling observed we also demonstrate that this type of behavior can be observed in real economic records and can be used to improve considerably risk estimation

indication of multiscaling in the volatility return intervals of stock markets a certain trend with the mean interval we generate surrogate records using the schreiber method and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most ranges of those substantial differences suggest that nonlinear correlations in the original volatility sequence account for the deviations from a single scaling law we also find that the original and surrogate records exhibit slight tendencies for short and long due to the discreteness and finite size effects of the records respectively to avoid as possible those effects for testing the multiscaling behavior we investigate the moments in the range 10100 and find that the exponent from the power law fitting m has a narrow distribution around 0 which depends on m for the 500 stocks the distribution of for the surrogate records are very narrow and centered around 0 this suggests that the return interval distribution exhibits multiscaling behavior due to the nonlinear correlations in the original volatility

multifractal detrended cross correlation analysis of carbon and crude oil markets abstract the complex dynamics between carbon and crude oil markets have been an increasingly interesting area of research in this paper we try to take a fresh look at the cross correlations between carbon and crude oil markets as well as their dynamic behavior employing multifractal detrended cross correlation analysis first we find that the return series of carbon and crude oil markets are significantly cross correlated second we confirm the existence of multifractality for the return series of carbon and crude oil markets by the multifractal detrended fluctuation analysis third based on the multifractal detrended cross correlation analysis we find the existence of power law cross correlations between carbon and crude oil markets the cross correlated behavior of small fluctuations is found to be more persistent than that of large fluctuations at last some relevant discussions and implications of the empirical results are presented

memory effects in the statistics of interoccurrence times between large returns in financial records we study the statistics of the interoccurrence times between events above some threshold q in two kinds of multifractal data sets multiplicative random cascades and multifractal random walks with vanishing linear correlations we show that in both data sets the relevant quantities probability density functions and the autocorrelation function of the interoccurrence times as well as the conditional return period are governed by power laws with exponents that depend explicitly on the considered threshold by studying a large number of representative financial records market indices stock prices exchange rates and commodities we show explicitly that the interoccurrence times between large daily returns follow the same behavior in a nearly quantitative manner we conclude that this kind of behavior is a general consequence of the nonlinear memory inherent in the multifractal data sets

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

monadic thue systems abstract certain infinite thue systems over a finite alphabet are studied in particular systems s e such that for each a e the set u u a s is a context freelanguage the syntactic structure of sets of ancestors and sets of descendants is considered as well as that of unions of congruence classes taken over infinite context free languages or regular sets the common descendant problem is shown to be tractable while the common ancestor problem is shown to be undecidable even for finite systems the word problem for confluent systems of this type is shown to be tractable the question of whether an infinite system of this type is confluent is shown to be undecidable as is the question of whether the congruence generated by such a system has a confluent presentation

on greibach normal form construction abstract we present an algorithm which given an arbitrary e free and chain free context free grammar produces an equivalent context free grammar in greibach normal form gnf this algorithm is a generalization of an algorithm recently presented by ehrenfeucht and rozenberg using this algorithm the well known gnf construction of rosenkrantz can be obtained furthermore it is possible to rewrite a given context free grammar by a gnf grammar which has at most twice as much nonterminals as the original grammar this result is shown to be optimal with respect to the number of nonterminals

some properties of the doi edwards and k bkz equations and operators abstract we prove uniqueness of smooth solutions for a one dimensional k bkz equation with degenerated constitutive functions and state an existence and uniqueness result our results apply to the doi edwards micro macro model in the case of a shear flow and under the independent alignment assumption we also prove that a k bkz related operator is invertible within the previous functional framework

refining the hierarchy of blind multicounter languages and twist closed trios we introduce the new families k r rbc of languages accepted in quasi realtime by one way counter automata having k blind counters of which at least r are reversal bounded it is proved that these families form a strict and linear hierarchy of semi afls within the the family blind m c1 of blind multicounter languages with generator c1 w a1 b1 w a1 w b1 this thereby combines the families blind and rbc from 13 to one strict hierarchy and generalizes and sharpens greibachs results the strict inclusions between the k counter families k r rbc are proved using linear algebra techniques we also study the language theoretic monadic operation twist 18 20 in connection with the semi afls of languages accepted by multicounter and multipushdown acceptors all restricted to reversal bounded behavior it is verified that the family k r rbc is twist closed if and only if r 0 in which case k 0 rbc m ck ck being the k fold shuffle of disjoint copies of c1 we characterize the family m pal of languages accepted in quasi realtime by nondeterministic one way reversal bounded multipushdown acceptors as the least twist closed trio mtwist pal generated by the set of palindromes pal w a b w wrev

generating all permutations by context free grammars in chomsky normal form let ln be the finite language of all n strings that are permutations of n different symbols n 1 we consider context free grammars gn in chomsky normal form that generate ln in particular we study a few families gn n 1 satisfying l gn ln for n 1 with respect to their descriptional complexity i e we determine the number of nonterminal symbols and the number of production rules of gn as functions of n

mathematical existence results for the doi edwards polymer model in this paper we present some mathematical results on the doi edwards model describing the dynamics of flexible polymers in melts and concentrated solutions this model developed in the late 1970s has been used and extensively tested in modeling and simulation of polymer flows from a mathematical point of view the doi edwards model consists in a strong coupling between the navier stokes equations and a highly nonlinear constitutive law the aim of this article is to provide a rigorous proof of the well posedness of the doi edwards model namely that it has a unique regular solution we also prove which is generally much more difficult for flows of viscoelastic type that the solution is global in time in the two dimensional case without any restriction on the smallness of the data

position restricted grammar forms and grammars this paper deals with the question of canonical types for grammar forms and grammars a grammar form is called position restricted of type m1 mn 1 if n 2 each m1 is a nonnegative integer and each production is either of the type 0 u u a terminal word or 0 w1 1w2 wn nwn 1 where each is a variable and each wi is a terminal word of length mi thus a grammar form is position restricted if all productions in it but the terminal ones have the same relative position of terminals and variables the main results are as follows each grammar form g1 is equivalent to a grammar form g2 of any desired position restricted type m1 mn 0 with the interpretation grammars of g2 of position restricted type m1 mn 0 being sufficient to define all languages in l g1 the above result is no longer true if the position restricted type is such that mn 1 1 the second main result is that each context free language is defined by a grammar g of any desired position restricted type

statistical analysis of the overnight and daytime return we investigate the two components of the total daily return close to close the overnight return close to open and the daytime return open to close as well as the corresponding volatilities of the 2215 new york stock exchange stocks for the 20 year period from 1988 to 2007 the tail distribution of the volatility the long term memory in the sequence and the cross correlation between different returns are analyzed our results suggest that i the two component returns and volatilities have features similar to that of the total return and volatility the tail distribution follows a power law for all volatilities and long term correlations exist in the volatility sequences but not in the return sequences ii the daytime return contributes more to the total return both the tail distribution and the long term memory of the daytime volatility are more similar to that of the total volatility compared to the overnight records in addition the cross correlation between the daytime return and the total return is also stronger iii the two component returns tend to be anticorrelated moreover we find that the cross correlations between the three different returns total overnight and daytime are quite stable over the entire 20 year period

power law for the calm time interval of price changes abstract in this paper we describe a newly discovered statistical property of time series data for daily price changes we investigated quantitatively the calm time intervals of price changes for 800 companies listed in the tokyo stock exchange and for the nikkei 225 index in the 27 year period from january 1975 to december 2001 a calm time interval is defined as the interval between two successive price changes above a fixed threshold we found that the calm time interval distribution of price changes obeys a power law decay furthermore we show that the power law exponent monotonically decreases with respect to the threshold

extreme times for volatility processes extreme times techniques generally applied to nonequilibrium statistical mechanical processes are also useful for a better understanding of financial markets we present a detailed study on the mean first passage time for the volatility of return time series the empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern the empirical mean first passage time to a certain level l is fairly different from that of the wiener process showing a dissimilar behavior depending on whether l is higher or lower than the average volatility all of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value we thus present the mean first passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description we discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential ornstein uhlenbeck model

theory of earthquakes interevent times applied to financial markets abstract we analyze the probability density function pdf of waiting times between financial loss exceedances the empirical pdfs are fitted with the self excited hawkes conditional poisson process with a long power law memory kernel the hawkes process is the simplest extension of the poisson process that takes into account how past events influence the occurrence of future events by analyzing the empirical data for 15 different financial assets we show that the formalism of the hawkes process used for earthquakes can successfully model the pdf of interevent times between successive market losses

analytic multivariate generating function for random multiplicative cascade processes institut fu r hochenergiephysik osterreichische akademie der wissenschaften nikolsdorf ergasse 18 a 1050 vienna austria 12 december 1997 chao dyn 9804024 we have found an analytic expression for the multivariategenerating function governing all n point statistics of randommultiplicative cascade processes the variable appropriate forthis generating function is the logarithm of the energy density ln rather than itself all cumulant statistics become sumsover derivatives of branching generating functions which arelaplace transforms of the splitting functions and completelydetermine the cascade process we show that the branch ing generating function is a generalization of the multifractalmass exponents two simple models from fully developedturbulence illustrate the new formalism 47 27 eq 02 50 sk 05 40 j

on the regularity of petri net languages petri nets are known to be useful for modeling concurrent systems once modeled by a petri net the behavior of a concurrent system can be characterized by the set of all executable transition sequences which in turn can be viewed as a language over an alphabet of symbols corresponding to the transitions of the underlying petri net in this paper we study the language issue of petri nets from a computational complexity viewpoint we analyze the complexity of theregularity problem i e the problem of determining whether a given petri net defines an irregular language or not for a variety of classes of petri nets includingconflict free trap circuit normal sinkless extended trap circuit bpp andgeneralpetri nets extended trap circuit petri nets are trap circuit petri nets augmented with a specific type ofcircuits as it turns out the complexities for these petri net classes range from nl nondeterministic logspace ptime polynomial time and np nondeterministic polynomial time to expspace exponential space in the process of deriving the complexity results we develop adecomposition approachwhich we feel is interesting in its own right and might have other applications to the analysis of petri nets as well as a by product an np upper bound of the reachability problem for the class of extended trap circuit petri nets which properly contains that of trap circuit and hence conflict free and bpp nets and is incomparable with that of normal and sinkless petri nets is derived

improved risk estimation in multifractal records application to the value at risk in finance we suggest a risk estimation method for financial records that is based on the statistics of return intervals between events above below a certain threshold q and is particularly suited for multifractal records the method is based on the knowledge of the probability w q t ensuremath delta t that within the next ensuremath delta t units of time at least one event above q occurs if the last event occurred t time units ago we propose an analytical estimate of w q and show explicitly that the proposed method is superior to the conventional precursory pattern recognition technique widely used in signal analysis which requires considerable fine tuning and is difficult to implement we also show that the estimation of the value at risk which is a standard tool in finances can be improved considerably by the method

levy walks and enhanced diffusion in milan stock exchange abstract we perform statistical analyses of the general and sectorial historical m i b indices of the milan stock exchange our analyses show that the price indices have statistical properties which are compatible with a levy random walk the time evolution of the daily variations of indices is intermittent on a time scale of years and the variance of almost all indices displays a superdiffusive behavior by using the theory of enhanced diffusion in levy walks as theoretical framework we ascribe the superdiffusive behavior to a nonlocal memory coupling price and time

statistics of return intervals in long term correlated records we consider long term correlated data with several distribution densities gaussian exponential power law and log normal and various correlation exponents ensuremath gamma 0l ensuremath gamma l1 and study the statistics of the return intervals r j between events above some threshold q we show that irrespective of the distribution the return intervals are long term correlated in the same way as the original record but with additional uncorrelated noise due to this noise the correlations are difficult to observe by the detrended fluctuation analysis which exhibits a crossover behavior but show up very clearly in the autocorrelation function the distribution p q r of the return intervals is characterized at large scales by a stretched exponential with exponent ensuremath gamma and at short scales by a power law with exponent ensuremath gamma ensuremath 1 we discuss in detail the occurrence of finite size effects for large threshold values for all considered distributions we show that finite size effects are most pronounced in exponentially distributed data sets where they can even mask the stretched exponential behavior in records of up to 10 6 data points finally in order to quantify the clustering of extreme events due to the long term correlations in the return intervals we study the conditional distribution function and the related moments we find that they show pronounced memory effects irrespective of the distribution of the original data

an easy proof of greibach normal form we present an algorithm which given an arbitrary a free context free grammar produces an equivalent context free grammar in 2 greibach normal form the upper bound on the size of the resulting grammar in terms of the size of the initially given grammar is given our algorithm consists of an elementary construction while the upper bound on the size of the resulting grammar is not bigger than the bounds known for other algorithms for converting context free grammars into equivalent context free grammars in greibach normal form

return intervals of rare events in records with long term persistence many natural records exhibit long term correlations characterized by a power law decay ofthe auto correlation function c s s with time lag s and correlation exponent 0 i i 1 we study how the presence ofsuch correlations a3ects the statistics ofthe return intervals rq for events above a certain threshold value q we 4nd that a the mean return interval rq does not depend on b the distribution of rq follows a stretched exponential ln pq r r rq and c the return intervals are also long term correlated with the exponent yielding clustering of both small and large return intervals we provide indications that both the stretched exponential behaviour and the clustering ofrare events can be seen in long temperature records c

forecasting volatility in shanghai and shenzhen markets based on multifractal analysis abstract this paper analyzes the multifractality in shanghai and shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis we find that the main source of multifractality is long range correlations of large and small fluctuations then we introduce a multifractal volatility measure mv and find that by taking mv as daily conditional volatility the simulated series displayed similar stylized facts to the original daily return series by capturing the dynamics of mv using the arfima model we find that the out of sample forecasting performance of the arfima mv model is better than some garch class models and the arfima rv model under some criteria of loss function

performance of multifractal detrended fluctuation analysis on short time series the performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono and multifractal models the reconstruction of the generalized hurst exponents is used to determine the range of applicability of the method and the precision of its results as a function of the decreasing length of the series as an application the series of the daily exchange rate between the us dollar and the euro is studied sets with known fractal and multifractal behavior the results are applied to the analysis of the daily exchange rate between the us dollar and the euro this time se ries is relatively short around 3500 entries given that the euro currency debuted at the beginning of 1999 further more in its short life the euro has gone through a dubita tive start followed by a strong couple of years and since around 2008 it has been immersed in a crisis which has threatened its existence this turbulent history makes it interesting to ask if its dynamics have changed with time the paper is organized as follows in the next section the mfdfa method is briefly described and the notation used in the rest of the paper is introduced section iii presents the analysis of the mono and multifractal syn thetic data section iv discusses the application of the results to a time series from finance namely the daily ex change rate between the us dollar and the euro finally the conclusions of this work are presented in section v

relaxation dynamics of aftershocks after large volatility shocks in the ssec index abstract the relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high frequency data sets of the shanghai stock exchange composite ssec index compared with previous relevant work we have defined main financial shocks based on large volatilities rather than large crashes we find that the occurrence rate of aftershocks with the magnitude exceeding a given threshold for both daily volatility constructed using 1 minute data and minutely volatility using intra minute data decays as a power law the power law relaxation exponent increases with the volatility threshold and is significantly greater than 1 taking financial volatility as the counterpart of seismic activity the power law relaxation in financial volatility deviates remarkably from the omori law in geophysics

finiteness conditions on subgroups and formal language theory we show in this article that the most usual finiteness conditions on a subgroup of a finitely generated group all have equivalent formulations in terms of formal language theory this correspondence gives simple proofs of various theorems concerning intersections of subgroups and the preservation of finiteness conditions in a uniform manner we then establish easily the theorems of greibach and of griffiths by considering free reductions of languages that describe the computations of pushdown automata in one case and of turing machines in the other thus making clear that they are essentially the same

a multifractal wavelet model with application to network traffic we develop a new multiscale modeling framework for characterizing positive valued data with long range dependent correlations 1 f noise using the haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results the model provides a rapid o n cascade algorithm for synthesizing n point data sets we study both the second order and multifractal properties of the model the latter after a tutorial overview of multifractal analysis we derive a scheme for matching the model to real data observations and to demonstrate its effectiveness apply the model to network traffic synthesis the flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics variance time plots and moment scaling and queuing behavior although for illustrative purposes we focus on applications in network traffic modeling the multifractal wavelet model could be useful in a number of other areas involving positive data including image processing finance and geophysics

recurrence time analysis long term correlations and extreme events the recurrence times between extreme events have been the central point of statistical analyses in many different areas of science simultaneously the poincar e recurrence time has been extensively used to characterize nonlinear dynamical systems we compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series in particular we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function on the interval whereto the recurrences are observed and on the temporal correlations of time series in the case of long term correlations we verify the validity of the stretched exponential distribution which is uniquely defined by the exponent ensuremath gamma at the same time showing that it is restricted to the class of linear long term correlated processes simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different ensuremath gamma which shows a lack of invariance under the change of observables

detrended fluctuation analysis on spot and futures markets of west texas intermediate crude oil abstract in this paper we study the auto correlations and cross correlations of west texas intermediate wti crude oil spot and futures return series employing detrended fluctuation analysis dfa and detrended cross correlation analysis dcca scaling analysis shows that for time scales smaller than a month the auto correlations and cross correlations are persistent for time scales larger than a month but smaller than a year the correlations are anti persistent while for time scales larger than a year the series are neither auto correlated nor cross correlated indicating the efficient operation of the crude oil markets moreover for small time scales the degree of short term cross correlations is higher than that of auto correlations using the multifractal extension of dfa and dcca we find that for small time scales the correlations are strongly multifractal while for large time scales the correlations are nearly monofractal analyzing the multifractality of shuffled and surrogated series we find that both long range correlations and fat tail distributions make important contributions to the multifractality our results have important implications for market efficiency and asset pricing models

scaling and memory of intraday volatility return intervals in stock markets we study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets including the standard and poor s 500 index and the 30 stocks that form the dow jones industrial index for different threshold q the probability density function pq tau scales with the mean interval tau as formula see text similar to that found in daily volatilities since the intraday records have significantly more data points compared to the daily records we could probe for much higher thresholds and still obtain good statistics we find that the scaling function f x is consistent for all 31 intraday data sets in various time resolutions and the function is well approximated by the stretched exponential f x similar to e ax gamma with gamma 0 38 0 05 and a 3 9 0 5 which indicates the existence of correlations we analyze the conditional probability distribution pq tau tau0 for tau following a certain interval tau0 and find pq tau tau0 depends on tau0 which demonstrates memory in intraday return intervals also we find that the mean conditional interval tau tau0 increases with tau0 consistent with the memory found for pq tau tau0 moreover we find that return interval records in addition to having short term correlations as demonstrated by pq tau tau0 have long term correlations with correlation exponents similar to that of volatility records

probability of large movements in financial markets abstract based on empirical financial time series we show that the silence breaking probability follows a super universal power law the probability of observing a large movement is inversely proportional to the length of the on going low variability period such a scaling law has been previously predicted theoretically r kitt j kalda physica a 353 2005 480 assuming that the length distribution of the low variability periods follows a multi scaling power law

global well posedness for a smoluchowski equation coupled with navier stokes equations in 2d we prove global existence for a nonlinear smoluchowski equation a nonlinear fokker planck equation coupled with navier stokes equations in 2d the proof uses a deteriorating regularity estimate in the spirit of 5 see also 1

improved surrogate data for nonlinearity tests current tests for nonlinearity compare a time series to the null hypothesis of a gaussian linear stochastic process for this restricted null assumption random surrogates can be constructed which are constrained by the linear properties of the data we propose a more general null hypothesis allowing for nonlinear rescalings of a gaussian linear process we show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity an iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution

griebach normal form transformation revisited we develop a new method for placing a given context free grammar into greibach normal form with only polynomial increase of its size starting with an arbitrarye free context free grammarg we transformginto an equivalent context free grammarhin extended greibach normal form i e in addition to rules fulfilling the greibach normal form properties the grammar can have chain rules the size ofhwill beo g 3 where g is the size ofg moreover in the case thatgis chain rule free hwill be already in greibach normal form ifhis not chain rule free then we use the standard method for chain rule elimination for the transformation ofhinto greibach normal form the size of the constructed grammar iso g 4

serial correlation of detrended time series a preliminary essential procedure in time series analysis is the separation of the deterministic component from the random one if the signal is the result of superposing a noise over a deterministic trend then the first one must estimate and remove the trend from the signal to obtain an estimation of the stationary random component the errors accompanying the estimated trend are conveyed as well to the estimated noise taking the form of detrending errors therefore the statistical errors of the estimators of the noise parameters obtained after detrending are larger than the statistical errors characteristic to the noise considered separately in this paper we study the detrending errors by means of a monte carlo method based on automatic numerical algorithms for nonmonotonic trends generation and for construction of estimated polynomial trends alike to those obtained by subjective methods for a first order autoregressive noise we show that in average the detrending errors of the noise parameters evaluated by means of the autocovariance and autocorrelation function are almost uncorrelated to the statistical errors intrinsic to the noise and they have comparable magnitude for a real time series with significant trend we discuss a recursive method for computing the errors of the estimated parameters after detrending and we show that the detrending error is larger than the half of the total error

multifractal random walk we introduce a class of multifractal processes referred to as multifractal random walks mrws to our knowledge it is the first multifractal process with continuous dilation invariance properties and stationary increments mrws are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio the mrws are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments we briefly explain how in the same way one can build stationary multifractal processes or positive random measures

missing data in aftershock sequences explaining the deviations from scaling laws in this paper we extend the branching aftershock sequence model to study the role of missing data at short times and small amplitudes after a mainshock we apply this model which contains three parameters characterizing the missing data to the magnitude and temporal statistics of four aftershock sequences in california we find that the observed time dependent deviations of the frequency magnitude scaling from the gutenberg richter power law dependency can be described quantitatively by the model we also show that for the same set of parameters the model is able to explain quantitatively the observed magnitude dependent deviations of the temporal decay of aftershocks from omori s law in addition we show that the same sets of data can also reproduce quite well the various functional forms of the probability density functions of the return times between consecutive events with magnitudes above a prescribed threshold as well as the violation of scaling at short and intermediate time scales

fractional calculus and continuous time finance ii the waiting time distribution we complement the theory of tick by tick dynamics of financial markets based on a continuous time random walk ctrw model recently proposed by scalas et al 4 and we point out its consistency with the behaviour observed in the waiting time distribution for bund future prices traded at liffe london

universal and non universal properties of recurrence intervals of rare events abstract this paper is devoted to the statistical analysis on the recurrence intervals of rare events that are defined above a given threshold the memory property of original records is found to have significant effects on the distribution and the correlation structure of recurrence intervals so that some universal and non universal properties arise i for long range persistent records by the arfima processes where large values are likely to follow large values the recurrence intervals yield stretched exponential distributions and further show long range persistence ii for long range anti persistent records by the arfima processes the recurrence intervals obey exponential distributions also absence of autocorrelation iii for short range autocorrelated records the distribution and the correlation structure of recurrence intervals both depend on the parameters of the model and the threshold of rare events

using string languages to describe picture languages a picture is a set of unit lines from the cartesian plane considered as a square grid a word over the alphabet l r u d is a picture description in the sense that it represents a traversal of a picture where the interpretation of the symbols l r u d is l go one unit line to the left of the current point r go one unit line to the right of the current point u go one unit line up from the current point and d go one unit line down from the current point a set of picture descriptions forms a picture description language this paper investigates the basic properties of pictures and picture description languages from the formal language theory point of view