On Solving Restoration Problem with Degenerated Diffusion by Separation Method

The suffient conditions of restoration problems' solvability in a class of the Ito stochastic differential 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) with the given properties of a movement, when a control is included into the coefficient of drift, are obtained by separation method. The structure of the control parameter is defined, ensuring sufficient conditions of the given integral manifold's existence of constructed equations' set in nonlinear and linear Problem statements.

inverse problems, stochastic differential equation, integral manifold