Cybernetics And Systems Analysis
International Theoretical Science
Journal
Abstract. General formulas are obtained for efficient calculation of optimal estimates for functionals of random processes with values in a Hilbert space. In a special case where the process under study is a solution of a nonlinear evolutionary differential equation with a small nonlinearity, the optimal estimates are expanded in powers of a small parameter and the expansion coefficients are given in the form of algorithms and calculated explicitly in terms of known quantities of the differential equation.
Keywords: algorithm, evolutionary differential equations, Radon–Nikodym density, extended stochastic integral, equivalence of measures, functional.
