Piecewise Deterministic Markov Processes and Semi-Dynamic Systems

Abstract

This paper focuses on the generalised piecewise deterministic Markov processes (PDMPs), introduced by Liu and Hou [14], and studies some properties of PDMPs connected with the characteristic triple. It is pointed out that Davis’ PDMP is the special case of the PDMP here, which restricts all the survivor functions so that they are absolutely continuous with respect to the time t. Furthermore, the state jump measure of a PDMP is introduced. When accompanied by the (state) transition kernal, it plays the same role to PDMPs as Q-matix to Q-processes.