Solvability of the master equation for dichotomous flow

Abstract

We consider the one-dimensional stochastic flow [formula presented] where [formula presented] 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 [formula presented] of the driven variable can be reduced to a differential equation of finite order. This generalizes the enumeration of the “solvable” cases. © 2001 The American Physical Society.