Piecewise-deterministic Markov process: Difference between revisions

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In [[probability theory]], a '''piecewise-deterministic Markov process (PDMP)''' is a process whose behaviour is governed by random jumps at points in time, but whose evolution is deterministically governed by an [[ordinary differential equation]] between those times. The class of models is "wide enough to include as special cases virtually all the non-diffusion models of [[applied probability]]."<ref name="davis" /> The process is defined by three quantities: the flowflow, the jump rate, and the transition measure.<ref name="siam2010">{{Cite journal | last1 = Costa | first1 = O. L. V. | last2 = Dufour | first2 = F. | doi = 10.1137/080718541 | title = Average Continuous Control of Piecewise Deterministic Markov Processes | journal = SIAM Journal on Control and Optimization | volume = 48 | issue = 7 | pages = 4262 | year = 2010 | pmid = | pmc = | arxiv = 0809.0477}}</ref>

The model was first introduced in a paper by [[Mark H. A. Davis]] in 1984.<ref name="davis">{{Cite journal | last1 = Davis | first1 = M. H. A. | authorlink = Mark H. A. Davis| title = Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models | journal = Journal of the Royal Statistical Society. Series B (Methodological)| volume = 46 | issue = 3 | pages = 353–388 | doi = 10.1111/j.2517-6161.1984.tb01308.x| jstor = 2345677| year = 1984 | pmid = | pmc = }}</ref>