On a method for an effective calculation of optimal estimates in problems of a filtration of random processes for certain nonlinear evolution differential equations in a Hilbert space

摘要

In the first part of this paper it is received the closed general expression which can be considered as algorithm for obvious calculation of an optimum estimation in problems of a filtration of random processes accepting the values in abstract Hilbert spaces. Using a condition of existence of density of Radon–Nikodym's measure generated by random process concerning some Gaussian measure (the optimum filter) it is shown that calculation of conditional mathematical expectation is reduced to calculation of an unconditional population mean on the base of obvious expressions.