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Average Optimality for Continuous-Time Markov Decision Processes Under Weak Continuity Conditions

Part of: Markov processes

Published online by Cambridge University Press:  30 January 2018

Yi Zhang
Yi Zhang*
Affiliation:
University of Liverpool
*
∗ Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK. Email address: yi.zhang@liv.ac.uk
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Abstract

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This paper considers the average optimality for a continuous-time Markov decision process in Borel state and action spaces, and with an arbitrarily unbounded nonnegative cost rate. The existence of a deterministic stationary optimal policy is proved under the conditions that allow the following; the controlled process can be explosive, the transition rates are weakly continuous, and the multifunction defining the admissible action spaces can be neither compact-valued nor upper semicontinuous.

Keywords

Continuous-time Markov decision processaverage optimalityweak continuity

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 954 - 970
Copyright
© Applied Probability Trust 

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