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Denumerable-state continuous-time Markov decision processes with unbounded transition and reward rates under the discounted criterion

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Xianping Guo  and
Weiping Zhu
Xianping Guo*
Affiliation:
Zhongshan University
Weiping Zhu*
Affiliation:
University of New South Wales
*
∗ Postal address: Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China.
∗∗ Postal address: School of Computer Science, ADFA, University of New South Wales, ACT 2600, Australia. Email address: [email protected]
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Abstract

In this paper, we consider denumerable-state continuous-time Markov decision processes with (possibly unbounded) transition and reward rates and general action space under the discounted criterion. We provide a set of conditions weaker than those previously known and then prove the existence of optimal stationary policies within the class of all possibly randomized Markov policies. Moreover, the results in this paper are illustrated by considering the birth-and-death processes with controlled immigration in which the conditions in this paper are satisfied, whereas the earlier conditions fail to hold.

Keywords

Continuous-time Markov decision process(possibly unbounded) transition and reward ratesdiscounted criterionoptimal stationary policy

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 90B50: Management decision making, including multiple objectives 60K99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 233 - 250
Copyright
Copyright © Applied Probability Trust 2002 

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