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

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 $g(x,t)=D(x)T(t)$, 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.

6 pages in LATEX code

References in corpus (1)

• Theory of the Relativistic Brownian Motion. The (1+1)-Dimensional Case

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