Learn More
On the central limit theorem for the sum of a random number of independent random variables, Z. [14] W. RICHTER, Limit theorems for sequences of random variables with sequences of random indices, Without assuming the homogeneity in time, processes indicated in the title of this paper were investigated in [13]. In our note, the results of [13] are applied to(More)
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)
1. A controlled Markov process with discrete time is considered. The aim of the control is to maximize the hverage reward over one step. Two criteria are studied" the lower limit of the average reward over one step (Criterion 1) and the upper limit of the average reward over one step (Criterion 2). In A. N. Shiryaev's paper [1] a summary of theorems on the(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)
  • 1