Finite dimensional Fokker-Planck equations for continuous time random walk limits

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Busani, Ofer¹ 

[1] Bar Ilan Univ, Ramat Gan, Israel

关键词: Continuous time random walk limits;    Fractional Fokker-Planck equation;    Anomalous diffusion;   

DOI  :  10.1016/j.spa.2016.08.008

来源: Elsevier

【 摘 要 】

Continuous Time Random Walk (CTRW) is a model where particle's jumps in space are coupled with waiting times before each jump. A Continuous Time Random Walk Limit (CTRWL) is obtained by a limit procedure on a CTRW and can be used to model anomalous diffusion. The distribution p (dx, t) of a CTRWL X-t satisfies a Fractional Fokker-Planck Equation (FFPE). Since CTRWLs are usually not Markovian, their one dimensional FFPE is not enough to completely determine them. In this paper we find the FFFEs of the distribution of Xt at multiple times, i.e. the distribution of the random vector (X-t1, ... , X-tn) for t(1) < ... < t(n) for a large class of CTRWLs. This allows us to define CTRWLs by their finite dimensional FFPEs. (c) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free