Piecewise-deterministic Markov process: Difference between revisions

Revision as of 22:41, 7 March 2013

Revision as of 15:57, 4 June 2013

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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 flow, the jump rate, and the transition measure.<ref name="siam2010">{{cite doi|10.1137/080718541}}</ref>

The model was first introduced in a paper by [[Mark H. A. Davis]] in 1984.<ref name="davis">{{cite jstor|2345677}}</ref>

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==Properties==

Löpker and Palmowski have shown conditions under which a [[reversed process|time reversed]] PDMP is a PDMP.<ref>{{cite doi|10.1214/EJP.v18-1958}}</ref> General conditions are known for PDMPs to be stable.<ref>{{cite doi|10.1137/060670109}}</ref>

==References==