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

Xin Guo, Alexey Piunovskiy, Yi Zhang

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1071-1088
Number of pages18
JournalJournal of Applied Probability
Volume54
Issue number4
DOIs
Publication statusPublished - 1 Dec 2017

Keywords

  • Continuous-time Markov decision process
  • discounted criterion

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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