Abstract
This paper deals with discrete-time Markov decision processes with
Borel state and action spaces. The criterion to be minimized is
the average expected costs, and the costs may have neither
upper nor lower bounds. In our former paper (to appear in Journal
of Applied Probability), weaker conditions are proposed
to ensure the existence of average optimal stationary policies. In
this paper, we further study some properties of optimal policies.
Under these weaker conditions, we not only obtain two
necessary and sufficient conditions for optimal policies, but also
give a semimartingale characterization of an average optimal
stationary policy.