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

Chapter Author(s) 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.