Piecewise-deterministic Markov process
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." The process is defined by three quantities: the ﬂow, the jump rate, and the transition measure.
PDMPs have been shown useful in ruin theory, queueing theory, for modelling biochemical processes such as subtilin production by the organism B. subtilis and DNA replication in eukaryotes for modelling earthquakes. Moreover, this class of processes has been shown to be appropriate for biophysical neuron models with stochastic ion channels.
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- Löpker, A.; Palmowski, Z. (2013). "On time reversal of piecewise deterministic Markov processes". Electronic Journal of Probability 18. arXiv:1110.3813. doi:10.1214/EJP.v18-1958.
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