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Some recent advances in theory and simulation of fractional diffusion processes. (English) Zbl 1166.45004

Summary: To offer an insight into the rapidly developing theory of fractional diffusion processes, we describe in some detail three topics of current interest: (i) the well-scaled passage to the limit from continuous time random walk under power law assumptions to space-time fractional diffusion, (ii) the asymptotic universality of the Mittag-Leffler waiting time law in time-fractional processes, (iii) our method of parametric subordination for generating particle trajectories.

MSC:

45K05 Integro-partial differential equations
26A33 Fractional derivatives and integrals
60G18 Self-similar stochastic processes
60G50 Sums of independent random variables; random walks
60G51 Processes with independent increments; Lévy processes
60J60 Diffusion processes

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