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1. Introduction. One of the major questions that occurs in investigating problems of dynamic programming on an infinite time interval is" in which natural classes of strategies do there exist strategies that produce a pay-off uniformly close to the pure value? It is known that in the case of finite state and control sets, optimal stationary strategies exist(More)
(Translated by Merle Ellis) 6. The main results. This paper is a continuation of [1]. Throughout we examine a homogeneous controlled Markov model d {X, A(.), p, r} with discrete time, count-able state space X, sets of controls A(x), x X, transition function p and payoff function r. For the initial state x X and strategy r H, where H is the set of all(More)
1. In this paper we consider the maximization of the average gain per unit step in controlled finite state Markov chains with compact control sets. In [1] and [2] a stationary optimal strategy was shown to exist under the assumption that the control sets are finite. In I-3] it was proved that if the control sets are compact and coincide with the transition(More)
In this paper we investigate the problem of optimal control of a Markov chain with a finite number of states when the control sets are compact in the metric space. The goal of the control is to maximize the average reward per unit step. For the case of finite control and state sets the existence of a stationary optimal policy was proved in [1] and [2]. In(More)
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