Eugene A. Fainberg

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In a non-homogeneous controllable Markov model with a total reward criterion, discrete time, infinite horizon and Borel spaces of states and controls, let a certain strategy 7r and an initial measure /x be given. In the paper the following two statements are proved: (a) (Theorem 3) for any K < +oo, there exists a non-randomized Markov strategy q such that >(More)
[13] J. R. BLUM AND J. R. ROSENBLATT, On the central limit theorem for the sum of a random number ofindependent random variables, Z. Wahrscheinlichkeitstheorie and Verw. Gebiete, 1, 4 (1962-1963), pp. 389-393. [14] W. RICHTER, Limit theorems for sequences ofrandom variables with sequences ofrandom indices, Theory Prob. Applications, 10 (1965), pp. 74-89.(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)
1] D. YLVISAKER,A note on the absence oftangencies in Gaussian samplepaths, Ann. Math. Statist., 39, (1968), pp. 261-262. [2] A. V. SKOROKHOD, A note on Gaussian measures in Banach space, Theory Prob. Applications, 15, 3 (1970), p. 508. [3] X. FERNIQUE, Intgrabilit des vecteurs gaussiens, C.R. Acad. Sci. Paris, Set. A, 270, 25 (1970), pp. 1698-1699. [4] H.(More)
In the theory of controlled Markov processes with discrete time we study, as a rule, controlled processes either with the total reward criterion or with criteria for mean reward per unit time. The theory of controlled Markov processes with Borel state and control spaces in the case of the total reward criterion was developed by D. Blackwell [1], [2] and R.(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)
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