On a class of exact solutions to the Fokker-Planck equations

Abstract

In this paper we study under which circumstances there exists a general change of gross variables that transforms any Fokker-Planck equation into another of the Ornstein-Uhlenbeck class that, therefore, has an exact solution. We find that any Fokker-Planck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associated with the diffusion is zero and the transformed drift is linear. We apply our criteria to the Kubo and Gompertz models. © 1982 American Institute of Physics.