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

elliptic problems with nonlinearities indefinite in sign abstract let r n n 3 be a bounded open set with smooth boundary and r we study the dirichlet problem formula with 1 q p and h k l nonnegative functions we prove existence nonexistence and multiplicity results depending on and according to the integrability properties of the ratio k p 1 h q 1

exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

discrepancy between subcritical and fast rupture roughness a cumulant analysis rough crack fronts in a sheet of paper obtained during a creep experiment do not follow true scaling laws local roughness exponents are estimated using the first order cumulant a quantity recently introduced in the turbulence literature j delour j f muzy and a arneodo eur phys j b 23 243 2001 using a large data set 102 fronts we find a significant difference in local roughness between the slow subcritical and the fast growth regime

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

local superlinearity and sublinearity for the p laplacian we study the existence nonexistence and multiplicity of positive solutions for a family of problems updelta p u f lambda x u u in w 0 1 p upomega where is a bounded domain in mathbb r n n p and 0 is a parameter the family we consider includes the well known nonlinearities of ambrosetti brezis cerami type in a more general form namely lambda a x u q b x u r where 0 leqslant q p 1 r leqslant p 1 here the coefficient a x is assumed to be nonnegative but b x is allowed to change sign even in the critical case preliminary results of independent interest include the extension to the p laplacian context of the brezis nirenberg result on local minimization in w 0 1 p text and c 0 1 a c 1 alpha estimate for equations of the form updelta p u h x u with h of critical growth a strong comparison result for the p laplacian and a variational approach to the method of upper lower solutions for the p laplacian

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

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

geometric and projection effects in kramers moyal analysis kramers moyal coefficients provide a simple and easily visualized method with which to analyze nonlinear stochastic time series one mechanism that can affect the estimation of the coefficients is geometric projection effects for some biologically inspired examples these effects are predicted and explored with a nonstochastic projection operator method and compared with direct numerical simulation of the systems langevin equations general features and characteristics are identified and the utility of the kramers moyal method is discussed projections of a system are in general non markovian but here the kramers moyal method remains useful and in any case the primary examples considered are found to be close to markovian

markov properties in presence of measurement noise recently several powerful tools for the reconstruction of stochastic differential equations from measured data sets have been proposed e g siegert et al phys lett a 243 275 1998 hurn et al j time series anal 24 45 2003 efficient application of the methods however generally requires markov properties to be fulfilled this constraint typically seems to be violated on small scales which frequently is attributed to physical effects on the other hand measurement noise such as uncorrelated measurement and discretization errors has large impacts on the statistics of measurements on small scales we demonstrate that the presence of measurement noise likewise spoils markov properties of an underlying markov process this fact is promising for the further development of techniques for the reconstruction of stochastic processes from measured data since limitations at small scales might stem from artificial noise sources rather than from intrinsic properties of the dynamics of the underlying process measurement noise however can be controlled much better than the intrinsic dynamics of the underlying process

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

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

combination of improved multibondic method and the wang landau method we propose a method for monte carlo simulation of statistical physical models with discretized energy the method is based on several ideas including the cluster algorithm the multicanonical monte carlo method and its acceleration proposed recently by wang and landau as in the multibondic ensemble method proposed by janke and kappler the present algorithm performs a random walk in the space of the bond population to yield the state density as a function of the bond number a test on the ising model shows that the number of monte carlo sweeps required of the present method for obtaining the density of state with a given accuracy is proportional to the system size whereas it is proportional to the system size squared for other conventional methods in addition the method shows a better performance than the original wang landau method in measurement of physical quantities

three dimensional antiferromagnetic q state potts models application of the wang landau algorithm we apply a newly proposed monte carlo method the wang landau algorithm to the study of the three dimensional antiferromagnetic q state potts models on a simple cubic lattice we systematically study the phase transition of the models with q 3 4 5 and 6 we obtain the finite temperature phase transition for q 3 and 4 whereas the transition temperature is down to zero for q 5 for q 6 there exists no order for any temperature we also study the ground state properties the size dependence of the ground state entropy is investigated we find that the ground state entropy is larger than the contribution from the typical configurations of the broken sublattice symmetry state for q 3 the same situations are found for q 4 5 and 6

dual monte carlo and cluster algorithms we discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model from the viewpoint of probability theory we detail the nature of a cluster algorithm make explicit the assumptions embodied in all clusters of which we are aware and define the construction of free cluster algorithms we also illustrate these procedures by rederiving the swendsen wang algorithm presenting the details of the loop algorithm for a worldline simulation of a quantum ital s 1 2 model and proposing a free cluster version of the swendsen wang replica method for the random ising model how the principle of maximum entropy might be used to aid the construction of cluster algorithms is also discussed

crossover and self averaging in the two dimensional site diluted ising model application of probability changing cluster algorithm using the newly proposed probability changing cluster pcc monte carlo algorithm we simulate the two dimensional 2d site diluted ising model since we can tune the critical point of each random sample automatically with the pcc algorithm we succeed in studying the sample dependent t c l and the sample average of physical quantities at each t c l systematically using the finite size scaling fss analysis for t c l we discuss the importance of corrections to fss both in the strong dilution and weak dilution regions the critical phenomena of the 2d site diluted ising model are shown to be controlled by the pure fixed point the crossover from the percolation fixed point to the pure ising fixed point with the system size is explicitly demonstrated by the study of the binder parameter we also study the distribution of critical temperature t c l its variance shows the power law l dependence l ensuremath n and the estimate of the exponent n is consistent with the prediction of aharony and harris phys rev lett 77 3700 1996 calculating the relative variance of critical magnetization at the sample dependent t c l we show that the 2d site diluted ising model exhibits weak self averaging

determining the density of states for classical statistical models a random walk algorithm to produce a flat histogram we describe an efficient monte carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models the density of states is modified at each step when the energy level is visited to produce a flat histogram by carefully controlling the modification factor we allow the density of states to converge to the true value very quickly even for large systems from the density of states at the end of the random walk we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature using this method we not only can avoid repeating simulations at multiple temperatures but we can also estimate the free energy and entropy quantities that are not directly accessible by conventional monte carlo simulations this algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability as with the multicanonical monte carlo technique our method overcomes the tunneling barrier between coexisting phases at first order phase transitions in this paper we apply our algorithm to both first and second order phase transitions to demonstrate its efficiency and accuracy we obtained direct simulational estimates for the density of states for two dimensional ten state potts models on lattices up to 200 x 200 and ising models on lattices up to 256 x 256 our simulational results are compared to both exact solutions and existing numerical data obtained using other methods applying this approach to a three dimensional j spin glass model we estimate the internal energy and entropy at zero temperature and using a two dimensional random walk in energy and order parameter space we obtain the rough canonical distribution and energy landscape in order parameter space preliminary data suggest that the glass transition temperature is about 1 2 and that better estimates can be obtained with more extensive application of the method this simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space

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

avalanche dynamics surface roughening and self organized criticality experiments on a three dimensional pile of rice we present a two dimensional system that exhibits features of self organized criticality the avalanches that occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution the critical exponents are ensuremath tau 1 21 2 for the avalanche size distribution and d 1 99 2 for the cutoff size furthermore the geometry of the avalanches is studied leading to a fractal dimension of the active sites of d b 1 58 2 using a set of scaling relations we can calculate the roughness exponent ensuremath alpha d ensuremath d b 0 41 3 and the dynamic exponent z d 2 ensuremath ensuremath tau 1 56 8 this result is compared with that obtained from a power spectrum analysis of the surface roughness which yields ensuremath alpha 0 42 3 and z 1 5 1 in excellent agreement with those obtained from the scaling relations

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

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

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

dynamics of driven interfaces near isotropic percolation transition we consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold in particular we study simple discrete forest fire lattice models through monte carlo simulations in two and three spatial dimensions an interface generated in the models is found to display complex behavior away from the percolation transition the interface is self affine with asymptotic dynamics consistent with the kardar parisi zhang universality class however in the vicinity of the percolation transition there is a different behavior at earlier times by scaling arguments we show that the global scaling exponents associated with the kinetic roughening of the interface can be obtained from the properties of the underlying percolation cluster our numerical results are in good agreement with theory however we demonstrate that at the depinning transition the interface as defined in the models is no longer self affine finally we compare these results with those obtained from a more realistic reaction diffusion model of slow combustion s1063 651x 98 08708 x

novel monte carlo algorithms and their applications abstract we describe a generalized scheme for the probability changing cluster pcc algorithm based on the study of the finite size scaling property of the correlation ratio the ratio of the correlation functions with different distances we apply this generalized pcc algorithm to the two dimensional 6 state clock model we also discuss the combination of the cluster algorithm and the extended ensemble method we derive a rigorous broad histogram relation for the bond number a monte carlo dynamics based on the number of potential moves for the bond number is proposed and applied to the three dimensional ising and 3 state potts models

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

broad histogram relation for the bond number and its applications we discuss monte carlo methods based on the cluster graph representation for spin models we derive a rigorous broad histogram relation bhr for the bond number a counterpart for the energy was derived by oliveira previously a monte carlo dynamics based on the number of potential moves for the bond number is proposed we show the efficiency of the bhr for the bond number in calculating the density of states and other physical quantities

scaling properties of the surface of the eden model in d 2 3 4 the surface of the eden model is investigated numerically by finite size scaling using a strip geometry three different versions are studied and it shows that the one mostly used previously exhibits strong finite size corrections in two dimensions it is found that the surface thickness simply grows as the square root of the width of the strip for infinitely long strips this result as well as the results in d 3 and d 4 suggest that the surface of the eden shares some properties with the equilibrium models used to describe the roughening transition moreover it is found that the surface thickness scales differently with the height of the cluster for infinitely large strips

superroughening versus intrinsic anomalous scaling of surfaces we study kinetically rough surfaces which display anomalous scaling in local properties such as the roughness or the height difference correlation function by studying the power spectrum of the surface and its relation to the height difference correlation we distinguish two independent causes for anomalous scaling one is superroughening global roughness exponent larger than or equal to 1 even if the spectrum behaves nonanomalously another cause is what we term an intrinsically anomalous spectrum in whose scaling an independent exponent exists which induces different scaling properties for small and large length scales we show that in this case the surface does not need to be superrough in order to display anomalous scaling the scaling relations we propose for the structure factor and height difference correlation for intrinsically anomalous surfaces are shown to hold for a random diffusion equation independently of the value of the global roughness exponent below or above one

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

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

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

existence and uniqueness of solutions of nonlinear neumann problems soit d r n un domaine connexe borne lisse et on suppose qu en chaque point x d la normale exterieure n est bien definie soit a une fonction arbitraire continue de holder dans d on etudie les solutions positives du probleme de neumann non lineaire u a x g u 0 dans d u n 0 sur d ou g r r est une fonction de classe c r c 1 r 0 1

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

exact diffusion constant for one dimensional asymmetric exclusion models the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions is considered on a ring of size n the steady state of this system is known all configurations have equal weight which allows for easy computation of the average velocity of a particle in the steady state here an exact expression for the diffusion constant of a particle is obtained for arbitrary number of particles and system size by using a matrix formulation two limits of infinite system size n are discussed firstly when the number of particles remains finite as n to infinity the diffusion constant remains dependent on the exact number of particles due to correlations between successive collisions secondly when the density p of particles is non zero i e when the number of particles is equal to n rho as n to infinity the diffusion constant scales as n 12 the exponent 1 2 is related to the dynamic exponent z 3 2 of the kpz equation in 1 1 dimensions

scaling and correlations in foreign exchange market abstract we observe that the distribution of the relative return describing the variation of a certain currency of 74 global currencies obeys a power law by using the random matrix theory we find that the distribution of eigenvalues of correlation matrix of relative return also follows a power law using a scaled factorial moment we investigate the distribution of correlation coefficients of the relative return and observe intermittence phenomenon furthermore we define the influence strength for a certain currency which reflects the influence of its price change to the community interested by doing that we find that the distribution of influence strength is again a power law beyond that we compare the influence strength of chinese yuan rmb to those of other seven important currencies which may have some interesting indications

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

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

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

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

multiple positive solutions for a class of concave convex elliptic problems in rn involving sign changing weight in this paper we study the multiplicity of positive solutions for the following concave convex elliptic equation u u f x uq 1 g x up 1in rn u 0in rn u h1 rn where 1 q 2 p 2 2 2nn 2 if n 3 2 if n 1 2 and the parameters 0 we assume that f x f x f x is sign changing and g x a x b x where the functions f a and b satisfy suitable conditions

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

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

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

multiple time scales and the empirical models for stochastic volatility abstract the most common stochastic volatility models such as the ornstein uhlenbeck ou the heston the exponential ou expou and hull white models define volatility as a markovian process in this work we check the applicability of the markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic to this end we consider the volatility at both short a few days and long a few months time scales as a markovian process and estimate for it the coefficients of the kramers moyal expansion using the data for dow jones index it has been found that the empirical data allow to take only the first two coefficients of expansion to be non zero that define form of the volatility stochastic differential equation of ito it proved to be that for the long time scale the empirical data support the expou model at the short time scale the empirical model coincides with expou model for the small volatility quantities only

fokker planck perspective on stochastic delay systems exact solutions and data analysis of biological systems stochastic delay systems with additive noise are examined from the perspective of fokker planck equations for a linear system the exact stationary probability density is derived by means of a delay fokker planck equation we show how to determine the delay equation of the linear system from experimental data and corroborate a fundamental result previously obtained by kuchler and mensch we also propose a method to derive delay equations of nonlinear systems from experimental data to this end the theory of multivariate fokker planck equations is used the applicability of this method is demonstrated for stochastic models describing tracking and pointing movements of humans

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

stochastic time series with strong correlated measurement noise markov analysis in n dimensions an extension and generalization of a recently presented approach for the analysis of langevin type stochastic processes in the presence of strong measurement noise is presented for a stochastic process in n dimensions which is superimposed with strong exponentially correlated gaussian distributed measurement noise it is possible to extract the strength and the correlation functions of the noise as well as polynomial approximations of the drift and diffusion functions of the underlying process

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

the nehari manifold for a semilinear elliptic equation with a sign changing weight function abstract the nehari manifold for the equation u x a x u x b x u x 1u x for x together with dirichlet boundary conditions is investigated exploiting the relationship between the nehari manifold and fibrering maps i e maps of the form t j tu where j is the euler functional associated with the equation we discuss how the nehari manifold changes as changes and show how existence and non existence results for positive solutions of the equation are linked to properties of the manifold

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

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

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

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

scaling properties of eden clusters in three and four dimensions we study the scaling properties of noise reduced eden clusters in three and four dimensions for variant b in the strip geometry we find that the width w for large times behaves as a s g lsd 1 where l is the width of the strip s the noise reduction parameter d the dimension of space and a s a decreasing function of s g is a scaling function with the property g u 12 as u 0 and g u ux as u where is the roughness exponent this scaling result leads to a new way of determining in 3 dimensions our numerical values for support a recent conjecture by kim and kosterlitz 2 d 2 and contradict all the former analytical conjectures in 4 dimensions we cannot distinguish between the conjectures of kim and kosterlitz and the conjecture of wolf and kertesz because large crossovers and finite size effects make the measurement of the exponents difficult

local superlinearity and sublinearity for indefinite semilinear elliptic problems in this paper the usual notions of superlinearity and sublinearity for semilinear problems like du f x u are given a local form and extended to indefinite nonlinearities here f x s is allowed to change sign or to vanish for s near zero as well as for s near infinity some of the well known results of ambrosetti bre zis cerami are partially extended to this context

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

probability changing cluster algorithm for potts models we propose a new effective cluster algorithm of tuning the critical point automatically which is an extended version of the swendsen wang algorithm we change the probability of connecting spins of the same type p 1 e j k b t in the process of the monte carlo spin update since we approach the canonical ensemble asymptotically we can use the finite size scaling analysis for physical quantities near the critical point simulating the two dimensional potts models to demonstrate the validity of the algorithm we have obtained the critical temperatures and critical exponents which are consistent with the exact values the comparison has been made with the invaded cluster algorithm

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

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

morphology and dynamic scaling analysis of cell colonies with linear growth fronts the growth of linear cell colony fronts is investigated from the morphology of cell monolayer colonies the cell size and shape distribution the front displacement velocity and the dynamic scaling analysis of front roughness fluctuations at the early growth stages colony patterns consist of rather ordered compact domains of small cells whereas at advanced stages an uneven distribution of cells sets in and some large cells and cells exhibiting large filopodia are produced colony front profiles exhibit overhangs and behave as fractals with the dimension d f 1 25 0 05 the colony fronts shift at 0 22 0 02 m min 1 average constant linear velocity and their roughness w increases with time t dynamic scaling analysis of experimental and overhang corrected growth profile data shows that w versus system width l log log plots collapse to a single curve when l exceeds a certain threshold value l o a width corresponding to the average diameter of few cells then the influence of overhangs on the roughness dynamics becomes negligible and a growth exponent 0 33 0 02 is derived from the structure factor analysis of overhang corrected profiles a global roughness exponent s 0 50 0 05 is obtained for l 200 m this set of exponents fulfills the family vicsek relationship it is consistent with the predictions of the continuous kardar parisi zhang model

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

on some indefinite and non powerlike elliptic equations abstract we consider a class of elliptic problems for the operator v acting on h 0 1 where is a bounded domain the main feature here is the indefinite behavior of both the operator and the nonlinearity based on the global geometry of the energy functional we prove the existence of two local minimizers and a mountain pass critical point for a concave convex type nonlinearity subcritical and critical growth are allowed on the nonlinearity

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