Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models
- 1 July 1984
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 46 (3) , 353-376
- https://doi.org/10.1111/j.2517-6161.1984.tb01308.x
Abstract
SUMMARY: A general class of non-diffusion stochastic models 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.Keywords
This publication has 12 references indexed in Scilit:
- Optimal control of piecewise deterministic markov processStochastics, 1985
- Average optimal policies in Markov decision drift processes with applications to a queueing and a replacement modelAdvances in Applied Probability, 1983
- Optimal control of service in tandem queuesIEEE Transactions on Automatic Control, 1982
- Some martingales associated with queueing and storage processesProbability Theory and Related Fields, 1981
- The Representation of Martingales of Jump ProcessesSIAM Journal on Control and Optimization, 1976
- Controlled jump processesStochastic Processes and their Applications, 1975
- A stochastic integral in storage theoryProbability Theory and Related Fields, 1971
- A theory of dams with continuous input and a general release ruleJournal of Applied Probability, 1969
- Markov ProcessesPublished by Springer Nature ,1965
- The analysis of non-Markovian stochastic processes by the inclusion of supplementary variablesMathematical Proceedings of the Cambridge Philosophical Society, 1955