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

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

2005-03-14

arxiv.org/abs/cond-mat/0503331v2

Physics

Condensed Matter

Soft Condensed Matter

6 pages in LATEX code

Scientific paper

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.

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