Random walk models associated with distributed fractional order differential equations

Umarov, Sabir, University of New Mexico; Steinberg, Stanly, University of New Mexico

doi:10.1214/074921706000000798

VOL. 51 | 2006 Random walk models associated with distributed fractional order differential equations

Sabir Umarov, Stanly Steinberg

Editor(s) Evarist Giné, Vladimir Koltchinskii, Wenbo Li, Joel Zinn

IMS Lecture Notes Monogr. Ser., 2006: 117-127 (2006) DOI: 10.1214/074921706000000798

Abstract

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a diffusion process in the sense of distributions is proved.