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Zbl 1166.45004
Gorenflo, Rudolf; Mainardi, Francesco
Some recent advances in theory and simulation of fractional diffusion processes. (English)
[J] J. Comput. Appl. Math. 229, No. 2, 400-415 (2009). ISSN 0377-0427

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 2000:: *45K05 Integro-partial differential equations
26A33 Fractional derivatives and integrals (real functions)
60G18 Self-similar processes
60G50 Sums of independent random variables
60G51 Processes with independent increments
60J60 Diffusion processes

Keywords: parametric subordination; random walks; anomalous diffusion; fractional calculus; renewal theory; power laws; Lévy processes; fractional diffusion processes; random walk; Mittag-Leffler waiting time law

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