Exact time dependent solutions to (1+1) Fokker-Planck equation via linearizing transformations to the Itô equations

Abstract

It is shown that invertible linearizing transformations of the one-dimensional Itô stochastic differential equations cast the associated Fokker-Planck equation to the heat equation. This leads to the time-dependent exact solutions to the Fokker-Planck equations via inverse transformations. To obtain the linearizing transformations of the Itô stochastic differential equation we have extended Gard's theorem to the timedependent case.