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Discretizations for the average impulse control of piecewise deterministic processes

Part of: Stochastic systems and control Markov processes

Published online by Cambridge University Press:  14 July 2016

O. L. V. Costa
O. L. V. Costa*
Affiliation:
Universidade de São Paulo
*
∗ Postal address: Departamento de Engenharia Eletrônica, Escola Politécnica da Universidade de São Paulo, 05508 900 São Paulo SP Brazil.
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Abstract

This paper presents a state space and time discretization for the general average impulse control of piecewise deterministic Markov processes (PDPs). By combining several previous results we show that under some continuity, boundedness and compactness conditions on the parameters of the process, boundedness of the discretizations, and compactness of the state space, the discretized problem will converge uniformly to the original one. An application to optimal capacity expansion under uncertainty is given.

Keywords

LONG-RUN COSTUNIFORM CONVERGENCE APPROXIMATION METHODSOPTIMIZATION PROBLEMSMARKOV DECISION MODELS'CAPACITY EXPANSION

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 90C40: Markov and semi-Markov decision processes 93E20: Optimal stochastic control
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 2 , June 1993 , pp. 405 - 420
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

This research was partially supported by the National Research Council — CNPq, Brazil, under grant 305173/88–0/EE/FV, and FAPESP (Research Council of the State of São Paulo), under grant 91/0508–3.

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