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) | x| -θ /2, the physical solutions for the probability distribution in the Ito, Stratonovich and postpoint discretization approaches can be obtained and analyzed.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.