Continuous time random walk models for fractional space-time diffusion equations

Sabir Umarov

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arXiv · 1409.4062

Continuous time random walk models for fractional space-time diffusion equations

Sabir Umarov

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Abstract

In this paper continuous time random walk models approximating fractional space-time diffusion processes are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change process is a L\'evy's stable subordinator with the stability index $\beta \in (0,1).$ In the parer the convergence of constructed CTRWs to time-changed processes associated with the corresponding fractional diffusion equations are proved using a new analytic method.

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Sabir Umarov. 2014-09-14. Continuous time random walk models for fractional space-time diffusion equations. https://arxiv.org/abs/1409.4062

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