Monte Carlo Random Walk Simulations Based on Distributed 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. Simulations based upon multi-term fractional order differential equations are performed.

18 pages. Submitted to Fractional Calculus and Applied Analysis

References in corpus (2)

• Numerical simulations of anomalous diffusion
• Random walk models associated with distributed fractional order differential equations