Recent results on conditions for the existence of average optimal stationary policies

This paper concerns countable state space Markov decision processes endowed with a (long-run expected) average reward criterion. For these models it summarizes and, in some cases, extends some recent results on sufficient conditions to establish the existence of optimal stationary policies. The topics considered are the following: (i) the new assumptions introduced by Sennott, (ii) necessary and sufficient conditions for the existence of a bounded solution to the optimality equation, and (iii) equivalence of average optimality criteria. Some problems are posed.