Discrete random walk models for space-time fractional diffusion

Details Discrete random walk models for space-time fractional diffusion Discrete random walk models for space-time fractional diffusion

2007-02-04

arxiv.org/abs/cond-mat/0702072v2

Chemical Physics, Vol. 284 No 1/2 (2002), pp. 521-541

Physics

Condensed Matter

Statistical Mechanics

38 pages, 8 figures (21 eps files), 1 Table

Scientific paper

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the {Cauchy} problem) of the fractional diffusion equations can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to a given fractional diffusion equation.

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