English

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

Soft Condensed Matter 2013-05-29 v2

Abstract

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)g(x,t)=D(x)T(t), and the behaviors of probability distributions, for some specific functions of D(x)D(x)% , are analyzed. In particular, for D(x)xθ/2D(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.

Keywords

Cite

@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}
}

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6 pages in LATEX code