| Abstract: | In this talk we consider the optimal stopping problem for semi-Markov processes (SMPs) under the expected discount criterion. By introducing an explicit construction of semi-Markov decision processes (SMDPs), we prove the equivalence between the expected discounted SMPs and SMDPs, that is, every stopping time of SMPs can induce a policy of SMDPs such that the value functions are equal, and vice versa. Then, the existence and computation of an optimal stopping time of SMPs are given by the equivalence relation and the SMDP theory. Moreover, we show that the optimal and epsilon-optimal stopping time can be characterized by the hitting time of the sets of special states. Finally, we illustrate our results by a maintenance system. |
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