Weak conditions for average optimality in Markov control processes

Considers the vanishing-discount-factor approach to investigate average optimality in Markov control processes with Borel state and action spaces. Under weak assumptions on the discounted differential value function the authors derive existence of average optimal stationary policies for initial states 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