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

✍ Scribed by E.A. Abdel-Rehim; R. Gorenflo

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 894 KB
Volume: 222
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.10.052

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✦ Synopsis

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 α-stable Lévy distribution, 0 < α < 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 (Lévy) noises. We simulate the continuous time random walk of these models by using the Monte Carlo method.

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