Abstract
We shall be concerned with the optimization problem of semi-Markov decision processes with countable state space and compact action space. Defined is the generalized reward function associated with the semi-Markov decision processes which include the ordinary discounted Markov decision processes of discrete time parameter and also the continuous time Markov decision processes. Main results are (a) the existence of an optimal stationary policy and (b) the relation between the maximal expected reward and the optimality equation. Also (c) some properties of the optimal staionary policy and the principle of optimality are obtained.
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