Solutions of the average cost optimality equation for Markov decision processes with weakly continuous kernel: The fixed-point approach revisited

Abstract

This paper shows the existence of lower semicontinuous solutions of the average cost optimality equation for Markov decision processes with Borel spaces, possible unbounded cost function and weakly continuous transition kernel. This is done imposing a growth condition on the cost function, a Lyapunov stability condition on the transition kernel and a set of standard compactness-continuity conditions. The solution of the average cost optimality equation is obtained by means of the Banach fixed-point theorem.