Uncoupled continuous-time random walk: finite jump length probability density function

In this work, the uncoupled continuous-time random walk model with the exponential jump length probability density function (PDF) is considered. Exact solutions for the PDF and second moment are obtained and investigated for different kinds of waiting-time PDF.

[1]  E. Barkai.  CTRW pathways to the fractional diffusion equation , 2001, cond-mat/0108024.

[2]  Melvin Lax,et al.  Stochastic Transport in a Disordered Solid. II. Impurity Conduction , 1973 .

[3]  E. Montroll,et al.  Anomalous transit-time dispersion in amorphous solids , 1975 .

[4]  Alvaro Corral.  Universal earthquake-occurrence jumps, correlations with time, and anomalous diffusion. , 2006, Physical review letters.

[5]  R. S. Mendes,et al.  A continuous time random walk model with multiple characteristic times , 2010 .

[6]  Karina Weron,et al.  Random walk models of electron tunneling in a fluctuating medium. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  E. Barkai,et al.  Fractional Fokker-Planck equation, solution, and application. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  M. Shlesinger.  Asymptotic solutions of continuous-time random walks , 1974 .

[9]  Enrico Scalas,et al.  Activity spectrum from waiting-time distribution , 2007, 0801.3043.

[10]  Marcin Kotulski,et al.  Asymptotic distributions of continuous-time random walks: A probabilistic approach , 1995 .

[11]  A. Kolomeisky,et al.  Simple mechanochemistry describes the dynamics of kinesin molecules , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[12]  V. Balakrishnan,et al.  Anomalous diffusion in one dimension , 1985 .

[13]  Guido Germano,et al.  Stochastic calculus for uncoupled continuous-time random walks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  D Sornette,et al.  Diffusion of epicenters of earthquake aftershocks, Omori's law, and generalized continuous-time random walk models. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Enrico Scalas,et al.  The application of continuous-time random walks in finance and economics , 2006 .

[16]  Jenny Nelson,et al.  Continuous-time random-walk model of electron transport in nanocrystalline TiO 2 electrodes , 1999 .

[17]  Marian Boguna,et al.  Long-tailed trapping times and Lévy flights in a self-organized critical granular system , 1997 .

[18]  K. S. Fa,et al.  Integrodifferential diffusion equation for continuous-time random walk. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  G. Weiss,et al.  Continuous-time random-walk model for financial distributions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Wojbor A. Woyczyński,et al.  Models of anomalous diffusion: the subdiffusive case , 2005 .

[21]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[22]  Barkai,et al.  From continuous time random walks to the fractional fokker-planck equation , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  J. Klafter,et al.  Crossover from Dispersive to Regular Transport in Biased Maps , 1997 .

[24]  Joseph Klafter,et al.  Derivation of the Continuous-Time Random-Walk Equation , 1980 .

[25]  Kwok Sau Fa,et al.  Continuous-time random walk: exact solutions for the probability density function and first two moments , 2011 .

[26]  E. Montroll,et al.  Random Walks on Lattices. II , 1965 .

[27]  Enrico Scalas,et al.  Mixtures of compound Poisson processes as models of tick-by-tick financial data , 2007 .

[28]  K. S. Fa.  Continuous-time random walk: crossover from anomalous regime to normal regime. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  R. Gorenflo,et al.  Fractional Calculus: Integral and Differential Equations of Fractional Order , 2008, 0805.3823.

[30]  Joseph Klafter,et al.  Probability Distributions for Continuous-Time Random Walks with Long Tails , 1994 .

[31]  Seong-Min Yoon,et al.  DYNAMICAL BEHAVIOR OF CONTINUOUS TICK DATA IN FUTURES EXCHANGE MARKET , 2002, cond-mat/0212393.

[32]  Brian Berkowitz,et al.  ANOMALOUS TRANSPORT IN RANDOM FRACTURE NETWORKS , 1997 .

[33]  Enrico Scalas,et al.  Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  R. Gorenflo,et al.  Fractional calculus and continuous-time finance II: the waiting-time distribution , 2000, cond-mat/0006454.