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Bias and Overtaking Optimality for Continuous-Time Jump Markov Decision Processes in Polish Spaces

Part of: Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Quanxin Zhu  and
Tomás Prieto-Rumeau
Quanxin Zhu*
Affiliation:
South China Normal University
Tomás Prieto-Rumeau*
Affiliation:
Universidad Nacional de Educación a Distancia
*
∗. Research partially supported by the Natural Science Foundation of China (10626021), the Natural Science Foundation of Guangdong Province (06300957), and CONACYT grant 45693-F.
∗. Research partially supported by the Natural Science Foundation of China (10626021), the Natural Science Foundation of Guangdong Province (06300957), and CONACYT grant 45693-F.
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Abstract

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In this paper we study the bias and the overtaking optimality criteria for continuous-time jump Markov decision processes in general state and action spaces. The corresponding transition rates are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. Under appropriate hypotheses, we prove the existence of solutions to the bias optimality equations, the existence of bias optimal policies, and an equivalence relation between bias and overtaking optimality.

Keywords

Continuous-time jump Markov decision processexpected average reward criteriongeneral state spacebias optimalityovertaking optimality

MSC classification

Secondary: 90C40: Markov and semi-Markov decision processes 93E20: Optimal stochastic control
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 417 - 429
Copyright
Copyright © Applied Probability Trust 2008 

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