ON THE CONVERGENCE OF EMPIRICAL ESTIMATES IN PROBLEMS OF STOCHASTIC PROGRAMMING FOR PROCESSES WITH DISCRETE TIME

dThis paper is devoted to the investigation of a stochastic programming problem with a convex criterion function in the case where the random factor is a stationary ergodic sequence. The problem is approximated by the problem of minimization of an empirical function. It is proved that, under some conditions, the empirical estimate coincides with the solution of the former problem in the case of a great number of observations and that the probability of large deviations of the empirical estimate from the solution of the initial problem decreases exponentially with increasing the number of observations.