On the continuous dependence of the stationary distribution of a piecewise deterministic Markov process on its jump intensity

Abstract

We examine a piecewise deterministic Markov process, whose whole randomness stems from the jumps, which occur at the random time points according to a Poisson process, and whose post-jump locations are attained by randomly selected transformations of the pre-jumps states. Between the jumps, the process is deterministically driven by a continuous semiflow. The aim of the paper is to establish the continuous dependence of the invariant measure of this process on the jump intensity.