Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach

Kwok Sau Fa

doi:10.1103/PhysRevE.72.020101

Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach

软凝聚态物质 2013-05-29 v2

作者: Kwok Sau Fa

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摘要

We consider the Langevin equation with multiplicative noise term which depends on time and space. The corresponding Fokker-Planck equation in Stratonovich approach is investigated. Its formal solution is obtained for an arbitrary multiplicative noise term given by $g(x,t)=D(x)T(t)$ , and the behaviors of probability distributions, for some specific functions of $D(x)$ % , are analyzed. In particular, for $D(x)\sim | x| ^{-\theta /2}$ , the physical solutions for the probability distribution in the Ito, Stratonovich and postpoint discretization approaches can be obtained and analyzed.

关键词

langevin dynamics anomalous diffusion partial differential equations

引用

@article{arxiv.cond-mat/0503331,
  title  = {Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach},
  author = {Kwok Sau Fa},
  journal= {arXiv preprint arXiv:cond-mat/0503331},
  year   = {2013}
}

备注

6 pages in LATEX code

Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach

摘要

关键词

引用

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