Piecewise-deterministic Markov process

"PDMP" redirects here. For prescription drug monitoring programs, see Prescription monitoring program.

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."[1] The process is defined by three quantities: the flow, the jump rate, and the transition measure.[2]

The model was first introduced in a paper by Mark H. A. Davis in 1984.[1]

  1. ^ a b Davis, M. H. A. (1984). "Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models". Journal of the Royal Statistical Society. Series B (Methodological). 46 (3): 353–388. doi:10.1111/j.2517-6161.1984.tb01308.x. JSTOR 2345677.
  2. ^ Costa, O. L. V.; Dufour, F. (2010). "Average Continuous Control of Piecewise Deterministic Markov Processes". SIAM Journal on Control and Optimization. 48 (7): 4262. arXiv:0809.0477. doi:10.1137/080718541. S2CID 14257280.