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A vanishing discount limit theorem for controlled Markov chains. (English) Zbl 0702.93066
Summary: Finite controlled Markov chains with discounted cost criterion are considered. It is proved that the average cost optimal control yields the stochastically smallest distribution of the discounted cost asymptotically as the discount rate tends to zero.

93E20 Optimal stochastic control
60J05 Discrete-time Markov processes on general state spaces
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