Fully discrete random walks for space-time fractional diffusion equations

For space-time fractional diffusion equations a theory of discrete-space discrete-time random walks, analogous to the theory of continuous-time random walks, is presented. The essential assumption is that the probabilities for waiting times and jump-widths behave asymptotically like powers with negative exponents related to the orders of the fractional derivatives. Properly scaled passage to the diffusion limit then leads to the space-time fractional diffusion equation. Illustrating examples are given, numerical results and plots of simulations are displayed.

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