The average cost optimality equation for Markov control processes on Borel spaces

Abstract

This paper deals with discrete-time Markov control processes with Borel state space, allowing unbounded costs and noncompact control sets. For these models, the existence of average optimal stationary policies has been recently established under very general assumptions, using an optimality inequality. Here we give a condition, which is a strengtened version of a variant of the ‘vanishing discount factor’ approach, for the optimality equation to hold.