Discrete random walk models for space-time fractional diffusion

Rudolf Gorenflo; Francesco Mainardi; Daniele Moretti; Gianni Pagnini; Paolo Paradisi

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Discrete random walk models for space-time fractional diffusion

Rudolf Gorenflo·Francesco Mainardi·Daniele Moretti·Gianni Pagnini·Paolo Paradisi

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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.

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BibTeX RIS

Rudolf Gorenflo, Francesco Mainardi, Daniele Moretti, Gianni Pagnini, Paolo Paradisi. 2007-09-25. Discrete random walk models for space-time fractional diffusion. https://arxiv.org/abs/cond-mat/0702072

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