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In this paper, we study asymptotic properties of problems of control ofstochastic discrete time systems (also known as Markov decision processes) withtime averaging and time discounting optimality criteria, and we establish thatthe Ces\`aro and Abel limits of the optimal values in such problems can beevaluated with the help of a certain infinite-dimensional linear programmingproblem and its dual.

LP Based Upper and Lower Bounds for Ces\`aro and Abel Limits of the Optimal Values in Problems of Control of Stochastic Discrete Time Systems