Stability Of Piecewise-deterministic Markov Processes

This paper is about the stability of PDMP. We often study the associated discrete-time Markov chain for the stability of PDMP. Davis and Costa(1990) studied it by its resolvent chain. Dufour and Costa(1999) overcame the defect of Davis'. However they all only studied the existence of an invariant measure for the PDMP X. They didn't study the detailed stability: irreducibility, regular, positive Harris recurrence, and unstability: non-positivity. In the paper we study the drift criterias of these forms of stability.PDMP was introduced by Davis.The distribution funtions of Davis' must be absolute continuity. Guoxin Liu first introduced the PDMP with discrete part and our results are for the PDMP with discrete part.