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Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models

M. H. A. Davis
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 46, No. 3 (1984), pp. 353-388
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2345677
Page Count: 36
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Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models
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Abstract

A general class of non-diffusion stochastic model is introduced with a view to providing a framework for studying optimization problems arising in queueing systems, inventory theory, resource allocation and other areas. The corresponding stochastic processes are Markov processes consisting of a mixture of deterministic motion and random jumps. Stochastic calculus for these processes is developed and a complete characterization of the extended generator is given; this is the main technical result of the paper. The relevance of the extended generator concept in applied problems is discussed and some recent results on optimal control of piecewise-deterministic processes are described.

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