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Continuous time random walk models for fractional space-time diffusion equations (1409.4062v1)
Published 14 Sep 2014 in math.PR, math-ph, and math.MP
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.