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

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 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 f with integral trajectories going to infinity.