Large Deviations of Empirical Estimates in the Stochastic Programming Problem for the Homogeneous Random Field with a Discrete Parameter

The problem of stochastic optimization is considered, where the random factor is a homogeneous, in a narrow sense, random field with a discrete parameter that satisfies the strong mixing condition. The primitive function of the criterion is replaced by an empirical one, based on observations of the field. According to the results of functional analysis and large deviations theory, large deviations of empirical estimates are investigated.