Kabanov, Y.Pergamenshchikov, S.2016-02-082016-02-0819970363-0129http://hdl.handle.net/11693/25678A 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 ε1/2. 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.EnglishAttainability setsControlled stochastic differential equationsHausdorff metricMayer problemSingular perturbationsTwo - scale systemArticle10.1137/S03630129942696851095-7138