On extension of stochastic constraints in the class of finitely additive probabilities

A construction of extension of stochastic constraints is considered. The authors find conditions of asymptotic nonsensibility (robustness) in the problem of constructing the domain of attainability “in mean” under the relaxation of stochastic constraints. For such domains, the regularization procedures compensating the nonmonotone perturbation of parameters in constraints are discussed. The article also deals with applications of the mentioned construction to investigation of the attainability domain of a dynamic system subjected to random perturbations, when the sample information about statistics of these perturbations is only given. Compactification of the space of countably additive probabilities is realized in the class of positive finitely additive measures of norm 1.