Piecewise-deterministic Markov process
In probability theory a piecewise-deterministic Markov process (PDMP) is a process whose behaviour is goverened by random jumps at points in time. Between each jump the evolution of the process is goverened by an ordinary differential equation. The class of models is "wide enough to include as special cases virtually all the non-diffusion models of applied probability."[1]
The model was first introduced in a paper by Mark H. A. Davis in 1984.[1]
Encapsulated models
Piecewise linear models such as the M/G/1 queue, the GI/G/1 queue and dam theory can be encapsulated as PDMPs with simple differential equations.[1]
Applications
PDMPs have been shown useful in ruin theory[2] and for modelling biochemical processes such as subtilin production by the organism B. subtilis and DNA replication in eukaryotes.[3]
References
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|jstor=1427443instead. - ^ Cassandras, Christos G.; Lygeros, John (2007). "9. Stochastic Hybrid Modeling of Biochemical Processes". Stochastic hybrid systems. CRC Press.
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