Stationary distributions for piecewise-deterministic Markov processes

Abstract

In this paper we show that the problem of existence and uniqueness of stationary distributions for piecewise-deterministic Markov processes (PDPs) is equivalent to the same problem for the associated Markov chain, so long as some mild conditions on the parameters of the PDP are satisfied. Our main result is the construction of an invertible mapping from the set of stationary distributions for the PDP to the set of stationary distributions for the Markov chain. Some sufficient conditions for existence are presented and an application to capacity expansion is given.