On the Behavior of One Stochastic Automaton in a Random Environment

A construction (behavior algorithm) of a finite stochastic automaton functioning in a stationary random environment with three classes of reactions (encouragement, punishment, indifference) is proposed. Using the methods of the theory of random walks, formulas are obtained for the generating function of the probability of changing the action and for calculating the probability characteristics of the behavior of an automaton. The convergence of sequences of finite automata (when the memory of the automaton n → ∞) to the corresponding infinite automaton (with a countable number of states) of a similar structure is established and given a classification of his possible behavior in this stationary random environment.