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Optimization of piecewise-deterministic Markov models

Published online by Cambridge University Press:  01 July 2016

M. H. A. Davis
M. H. A. Davis*
Affiliation:
Imperial College, London
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Extract

Piecewise-deterministic (PD) Markov processes consist of a mixture of deterministic motion and random jumps, the jumps occurring ‘spontanteously’ in a Poisson-like fashion and also ‘surely’ when the process hits certain boundaries. They form a flexible class of stochastic models, including as special cases almost all the non-diffusion models of applied probability. The construction of these processes will be outlined and precise characterization of the extended generator given.

Type
Applied Probability in Biology and Engineering. An ORSA/TIMS Special Interest Meeting
Information
Advances in Applied Probability , Volume 16 , Issue 1 , March 1984 , pp. 14
Copyright
Copyright © Applied Probability Trust 1984 

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References

Vinter, R. B. and Lewis, R. M. (1978) A necessary and sufficient condition for optimality of dynamic programming type, making no a priori assumptions on the controls. SIAM J. Control and Optimization 16, 571–583.CrossRefGoogle Scholar