Discrete random walk models for space-time fractional diffusion
Abstract
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.
Cite
@article{arxiv.cond-mat/0702072,
title = {Discrete random walk models for space-time fractional diffusion},
author = {Rudolf Gorenflo and Francesco Mainardi and Daniele Moretti and Gianni Pagnini and Paolo Paradisi},
journal= {arXiv preprint arXiv:cond-mat/0702072},
year = {2007}
}
Comments
38 pages, 8 figures (21 eps files), 1 Table