Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications in Cell Biology

Authors

Erik Andries, University of New Mexico
Sabir Umarov, University of New HavenFollow
Stanly Steinberg, University of New Mexico

Author URLs

Professor Umarov's Faculty's Profile

Document Type

Article

Publication Date

2006

Subject: LCSH

Random walks (Mathematics), Differential equations, Monte Carlo method

Disciplines

Mathematics

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.

Comments

This is the article published in Fractional Calculus and Applied Analysis, The original posting is found at https://eudml.org/doc/11288.

Repository Citation

Andries, Erik; Umarov, Sabir; and Steinberg, Stanly, "Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications in Cell Biology" (2006). Mathematics Faculty Publications. 15.
https://digitalcommons.newhaven.edu/mathematics-facpubs/15

Publisher Citation

Andries, Erik & Umarov, Sabir & Steinberg, Stanly. (2006). Monte Carlo random walk simulations based on distributed order differential equations with applications to cell biology. Fractional Calculus and Applied Analysis, 9(4), 351–369.