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

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

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Article ID: iaor200948280
Country: United States
Volume: 32
Issue: 1
Start Page Number: 73
End Page Number: 87
Publication Date: Feb 2007
Journal: Mathematics of Operations Research
Authors:
Abstract:

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.

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