We consider the discrete-time stochastic control problem for controlled Markov processes (CMP), with an average cost criterion. We show how structural properties in the model can be used to obtain a functional characterization of optimal values and policies, in the form of an average cost optimality equality (ACOE). In particular, Convex CMP are defined as those models for which the (discounted) value functions are convex. This convexity is used to obtain the ACOE as a limit of the

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... discountcd optimality equations, as the discounting vanishes, i.e. as the discount factor tends to one. We further comment on the potential algorithmic impact of this and other structured solutions.