Order reduction of optimal estimation problem for Langevin equation

The question under discussion in this paper is the optimal estimation for singular perturbed Langevin equation. On the basis of assumptions about parameters and conditions where the movement is performed, we choose three cases which have curtain peculiarities during the reduction of the optimal estimation problem. For order reduction task the theoretical method of integral manifolds is used. It allows to get the solution of Riccati equations for covariance matrix of the filter and build the corrected Kalman–Bucy filter of a lower dimension.