Simulation of the continuous time random walk of the space-fractional diffusion equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:222

Article

Abdel-Rehim, E. A.¹  Gorenflo, R.² 

[1] Suez Canal Univ, Dept Math & Comp Sci, Ismailia, Egypt

[2] Free Univ Berlin, Dept Math & Comp Sci, D-14195 Berlin, Germany

关键词: Fractional diffusion;    Space-Fractional derivative;    Fokker-Planck equation;    Stochastic processes;    alpha-stable distribution;    Continuous time random walk;    Monte Carlo method;   

DOI  :  10.1016/j.cam.2007.10.052

来源: Elsevier

【 摘 要 】

In this article, we discuss the solution of the space-fractional diffusion equation with and without central linear drift in the Fourier domain and show the strong connection between it and the alpha-stable Levy distribution, 0 < alpha < 2. We use some relevant transformations of the independent variables x and t, to find the solution of the space-fractional diffusion equation with central linear drift which is a special form of the space-fractional Fokker-Planck equation which is useful in studying the dynamic behaviour of stochastic differential equations driven by the non-Gaussian (Levy) noises. We simulate the continuous time random walk of these models by using the Monte Carlo method. (c) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free