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Title: Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology
Authors: Andries, Erik
Umarov, Sabir
Steinberg, Stanly
Keywords: Random Walk
Anomalous Diffusion
Confined Diffusion
Distributed Order Differential Equation
Monte-Carlo Simulation
Issue Date: 2006
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 9, No 4, (2006), 351p-369p
Abstract: In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for DODE. The scaling limits of the constructed random walks to a diffusion process in the sense of distributions is proved.
Description: Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37
ISSN: 1311-0454
Appears in Collections:2006

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