Abstract.

The sufficient conditions are obtained on the restoration problems solvability in a class of the stochastic differential Ito systems of the first order (with random disturbances from a class of Wiener processes and the diffusion degenerated with regard to a part of variables) on the given properties of a movement, when a control is included into the coefficient of drift, by separation method. The aspect of driving parameters is defined, ensuring sufficient conditions of the given integral manifold’s existence of constructed equations set in nonlinear and linear cases.

Keywords:

stochastic differential equations, integral manifold, restoration problem.