Some recent advances in theory and simulation of fractional diffusion processes

To offer a view into the rapidly developing theory of fractional diffusion processes we describe in some detail three topics of present 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.
Comment: 33 pages, 3 Figures, 5 eps files. Second International Workshop on Analysis and Numerical Approximation of Singular Problems (IWANASP 2006), 6-8 September 2006, Aegean University in Karlovassi, Samos, Greece