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.
"[1] The process is defined by three quantities: the flow, the jump rate, and the transition measure.
[1] PDMPs have been shown useful in ruin theory,[3] queueing theory,[4][5] for modelling biochemical processes such as DNA replication in eukaryotes and subtilin production by the organism B. subtilis,[6] and for modelling earthquakes.
[7] Moreover, this class of processes has been shown to be appropriate for biophysical neuron models with stochastic ion channels.
(For instance, they used the density of a trajectories to perform importance sampling, this work was further developed by Chennetier and Al.[12] to estimate the reliability of industrial systems.)