Conditionally optimal filtering and extrapolation of continuous processes

An extension in given of the theory previously developed by the author of conditionally optimal estimation and extrapolation of processes determined by stochastic differential equations. This extension is based upon a new method of defining classes of admissible filters and extrapolators. This new approach permits one to include any given filter described by differential equations into the corresponding class of admissible filters providing thus the possibility of estimating the accuracy of any such filter and improving it by optimization of the coefficients of the differential equation.