Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation

Daniel Fulger, Enrico Scalas, Guido Germano

Risultato della ricerca: Contributo su rivistaArticolo in rivistapeer review

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 originaleInglese
Numero di articolo021122
RivistaPhysical Review E
Volume77
Numero di pubblicazione2
DOI
Stato di pubblicazionePubblicato - 25 feb 2008
Pubblicato esternamente

Fingerprint

Entra nei temi di ricerca di 'Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation'. Insieme formano una fingerprint unica.

Cita questo