Continuous Time Markov Decision Processes with Unbounded Rewards under the Discounted Criterion

This paper investigates the continuous time Markov decision processes with discounted criterion.Here, the state spacc and the action set are countable, the reward functions are unbounded,and the transition rates are uniformly bounded. A new condition about the unbounded rewards ispresented. In a new set of Markov policies, what is true under bounded rewards has been provedis eaually ture under unbounded rewards. Through the study of the intrinsic structures of optimalplicies, a condition necessary and sulflicient for optinal policies is first worked out.