Solvability of the master equation for dichotomous flow

Abstract

We consider the one-dimensional stochastic flow (x) over dot = f(x) + g(x)xi(t), where xi(t) is a dichotomous Markov noise, and use a simple procedure to identify the conditions under which the integro-differential equation satisfied by the total probability density P(x,t) of the driven variable can be reduced to a differential equation of finite order. This generalizes the enumeration of the "solvable" cases.