Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations
Dynamical Systems
2007-05-23 v1
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.
Cite
@article{arxiv.math/0606797,
title = {Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations},
author = {Erik Andries and Sabir Umarov and Stanly Steinberg},
journal= {arXiv preprint arXiv:math/0606797},
year = {2007}
}
Comments
18 pages. Submitted to Fractional Calculus and Applied Analysis