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On time reversal of piecewise deterministic Markov processes. (English) Zbl 1294.60099
The aim of this paper is to introduce the time reversal of a general piecewise deterministic Markov process (PDMP). Given a stationary version \({X_t}\) of such a process, the authors let \(X_t^ * = {X_{(T - t) - }}\) and study the characteristics of this reversed process. The paper is divided into four sections. In the first section, after recalling the definition of PDMPs, the authors investigate the embedded Markov chains. In Section 2 they define the reversed Markov process and show that it is a PDMP. Section 3 is devoted to PDMPs on the real line. The authors give an integral equation for the stationary distribution and study several examples. In Section 4 they discuss the time reversal of a fluid model.

MSC:
60J25 Continuous-time Markov processes on general state spaces
60G05 Foundations of stochastic processes
60K25 Queueing theory (aspects of probability theory)
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