Chornej R. Problems of Markov processes control with an aftereffect

The disertation is devoted to Markov fields control on graphs. Reculiarity is definition of Markov property, that is, the state of a certain vertex depends on state of its full neiborhood and its decision at a previous moment. Actuality of given method of approach to definition of Markov property is shown. It is proved that optimal strategy in problem of minimizing of average expenses functional per time unit in case of finite action space and finite phase space we can choose in nonrandomized homogeneous strategy class. If phase space and action space are infinite for problem of one vertex control and problem of transition of control from vertex to vertex sufficient conditions of existence of optimal nonrandomized stationary strategies and a some probabilities of these sufficient conditions for average cost criteria per time unit are obtained. Sufficient conditions of existence of nonrandomized stationary strategy and a game value is identically equal to a constant for both Players in stochastic game o n graph is obtained.