ON THE RESTORATION PROBLEM WITH DEGENERATED DIFFUSION

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.