WEAK CONDITIONS FOR AVERAGE OPTIMALITY IN MARKOV CONTROL PROCESSES

In this paper we study the existence of average cost optimal policies for Markov control processes on Borel spaces and with possibly unbounded costs and controls. Under assumptions weaker than those used in the previous literature, we show that the 'optimality inequality' holds everywhere, and that there exists a stationary policy which is optimal whenever the initial state lies in a possibly proper subset of the state space. This is in contrast to previous works where an implicit 'unichain' assumption ensures optimality for all initial states.