An Explicit Solution to the Fokker-Planck Equation for an Ordinary Differential Equation†

Abstract

An explicit, steady–state solution is found to the Fokker–Planck equation for an nth order, ordinary linear differential equation with constant coefficients excited by a single white noise source by making use of a Liapunov function. Liapunov functions are also used to derive a more general result of Wang and Uhlenbeck.