This article is cited in 1 paper

Stationary Fokker–Planck equation on noncompact manifolds and in unbounded domains

A. I. Noarov

Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

Abstract: We investigate the Fokker–Planck equation on an infinite cylindrical surface and in an infinite strip with reflecting boundary conditions, prove the existence of a positive (not necessarily integrable) solution, and derive various conditions on the vector field $\mathbf f$ that are sufficient for the existence of a solution that is the probability density. In particular, these conditions are satisfied for some vector fields $\mathbf f$ with integral trajectories going to infinity.

Keywords: diffusion process, stationary distribution, elliptic equation for measures, averaging method.

Received: 04.03.2015
Revised: 01.02.2016

DOI: 10.4213/tmf8885

 English version: Theoretical and Mathematical Physics, 2016, 189:3, 1796–1805

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