Abstract
We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Lévy α -stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Lévy α -stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.
Lingua originale | Inglese |
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Numero di articolo | 021122 |
Rivista | Physical Review E |
Volume | 77 |
Numero di pubblicazione | 2 |
DOI | |
Stato di pubblicazione | Pubblicato - 25 feb 2008 |
Pubblicato esternamente | Sì |