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Sample-path optimality and variance-minimization of average cost Markov control processes. (English) Zbl 0951.93074

The authors study several average cost criteria for discrete-time, stationary Markov control processes on Borel spaces. Costs may be unbounded. They show the existence of a sample-path average cost (SPAC) optimal stationary policy. They also prove that a stationary policy is SPAC optimal iff it is expected average cost (EAC) optimal and the existence of a stationary SPAC optimal (or equivalently EAC optimal) policy with minimal limiting variance.
The SPAC case considered in the paper has been rarely discussed in the literature in comparison with average cost (AC) cases. The bibliography contains 37 items.

MSC:

93E20 Optimal stochastic control
90C40 Markov and semi-Markov decision processes
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