On correct extension of some stochastically constrained problems (Q1285444)

Insensitivity of various control and optimization problems under perturbations of stochastic constraints are discussed. Efficiently checked conditions characterizing asymptotic insensitivity under perturbations of the system of stochastic constraints are established. In the proofs of the results the methods of topology, stochastic processes and optimization theory are extensively used. The problems of asymptotic attainability and admissible controls are also discussed. Simple illustrative examples are presented. Moreover, the paper contains several remarks and comments concerning stochastically constrained problems in control theory and optimization. Similar problems have been recently considered in the monograph [\textit{A. G. Chentsov}, Asymptotic attainability, Dordrecht/Kluwer (1997; Zbl 0859.93002)].