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Note on discounted continuous-time Markov decision processes with a lower bounding function

Part of: Markov processes

Published online by Cambridge University Press:  30 November 2017

Xin Guo ,
Alexey Piunovskiy  and
Yi Zhang
Xin Guo*
Affiliation:
University of Liverpool
Alexey Piunovskiy*
Affiliation:
University of Liverpool
Yi Zhang*
Affiliation:
University of Liverpool
*
* Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.
* Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.
* Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.
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Abstract

We consider the discounted continuous-time Markov decision process (CTMDP), where the negative part of each cost rate is bounded by a drift function, say w, whereas the positive part is allowed to be arbitrarily unbounded. Our focus is on the existence of a stationary optimal policy for the discounted CTMDP problems out of the more general class. Both constrained and unconstrained problems are considered. Our investigations are based on the continuous-time version of the Veinott transformation. This technique has not been widely employed in the previous literature on CTMDPs, but it clarifies the roles of the imposed conditions in a rather transparent way.

Keywords

Continuous-time Markov decision processdiscounted criterion

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 4 , December 2017 , pp. 1071 - 1088
Copyright
Copyright © Applied Probability Trust 2017 

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