Random walk models associated with distributed fractional order differential equations

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.

Published at http://dx.doi.org/10.1214/074921706000000798 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• The fundamental solution of the space-time fractional diffusion equation
• Multifractal random walk in copepod behavior
• A Model for Ordinary Levy Motion

Cited by in corpus (4)

• SDEs driven by a time-changed Lévy process and their associated time-fractional order pseudo-differential equations
• A generalization of the central limit theorem consistent with nonextensive statistical mechanics
• Stability of fractional-order linear time-invariant system with noncommensurate orders
• Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations