Average cost Markov decision processes under the hypothesis of Doeblin

Average cost Markov decision processes (MDPs) with compact state and action spaces and bounded lower semicontinuous cost functions are considered. Kurano has treated the general case in which several ergodic classes and a transient set are permitted for the Markov process induced by any randomized stationary policy under the hypothesis of Doeblin and showed the existence of a minimum pair of state and policy. This paper considers the same case as that discussed in Kurano and proves some new results which give the existence theorem of an optimal stationary policy under some reasonable conditions.