Continuous-time Markov decision processes with discounted rewards: The case of Polish spaces

• 成果类型: Article
• 署名作者: Guo, Xianping
• 署名单位: Sun Yat Sen University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1060.0210
• 发表日期: 2007
• 页码: 73-87
• 关键词: bias optimality; countable state; THEOREMS; chains; rates

摘要

This paper deals with continuous-time Markov decision processes in Polish spaces, under an expected discounted reward criterion. The transition rates of underlying continuous-time jump Markov processes are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. We first give conditions on the controlled system's primitive data. Under these conditions we prove that the transition functions of possibly nonhomogeneous continuous-time Markov processes are regular by using Feller's construction approach to such transition functions. Then, under additional continuity and compactness conditions, we ensure the existence of optimal stationary policies by using the technique of extended infinitesimal operators associated with the transition functions, and also provide a recursive way to compute (or at least to approximate) the optimal reward values. Finally, we use examples to illustrate our results and the gap between our conditions and those in the previous literature.