On the connection between exponential ergodicity of a piecewise deterministic Markov process and the chain given by its post-jump locations

Abstract

The aim of this paper is to derive the exponential ergodicity in the Wasserstein distance for a piecewise-deterministic Markov process (PDMP), being typically encountered in biological models, defined via interpolation of some discrete-time Markov chain. The key idea of the presented approach is to show that existence of an appropriate Markovian coupling between two instances of the chain implies that the transition semigroup associated with the continuous-time process is exponentially contracting.