Weak conditions for the existence of optimal stationary policies in average Markov decision chains with unbounded costs

Average cost Markov decision chains with discrete time parameter are considered. The cost function is unbounded and satisfies an additional condition which frequently holds in applications. Also, we assume that there exists a single stationary policy for which the corresponding Markov chain is irreducible and ergodic with finite average cost. Within this framework, the existence of an average cost optimal stationary policy is proved.