Finite-state approximation of Markov decision processes with unbounded costs and Borel spaces

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Computing optimal policies for stochastic control problems with general state and action spaces is often intractable. This paper studies finite-state approximations of discrete time Markov decision processes (MDPs) with Borel state and action spaces and unbounded one-stage cost function, for both discounted and average cost criteria. Under mild technical assumptions, it is shown that stationary optimal policies obtained from the solutions to finite-state models can approximate an optimal stationary policy with arbitrary precision. A simulation example is provided.