Piecewise-deterministic Markov process
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The model was first introduced in a paper by Mark H. A. Davis in 1984.
Examples
Piecewise linear models such as Markov chains, continuous-time Markov chains, the M/G/1 queue, the GI/G/1 queue and the fluid queue can be encapsulated as PDMPs with simple differential equations.
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Applications
PDMPs have been shown useful in ruin theory, queueing theory, for modelling biochemical processes such as DNA replication in eukaryotes and subtilin production by the organism B. subtilis, and for modelling earthquakes. Moreover, this class of processes has been shown to be appropriate for biophysical neuron models with stochastic ion channels.
Properties
Löpker and Palmowski have shown conditions under which a time reversed PDMP is a PDMP. General conditions are known for PDMPs to be stable.
Galtier et al. studied the law of the trajectories of PDMP and provided a reference measure in order to express a density of a trajectory of the PDMP. Their work opens the way to any application using densities of trajectory. (For instance, they used the density of a trajectories to perform importance sampling, this work was further developed by Chennetier and Al. to estimate the reliability of industrial systems.)