ON CONVERGENCE OF ATTAINABILITY SETS FOR CONTROLLED TWO-SCALE STOCHASTIC LINEAR SYSTEMS

摘要

A limit of attainability sets is found for a linear two-scale stochastic system for the case when the diffusion coefficient of the fast variable is of order epsilon(1/2). The attainability set is defined as the set of distributions of attainable terminal values of solutions of stochastic differential equations. As a corollary we calculate a limit of the optimal value of the terminal cost in the stochastic Mayer problem. [References: 20]