Abstract
A general formula for effective calculations of optimal estimates for functionals of solutions of a certain nonlinear evolution differential equations in a Hilbert space H are received. In particular, when the actual process is the solution of some nonlinear evolution differential equation with a small nonlinearity, the obtained optimal estimates expend by powers of small parameter and the coefficients of this expansion are expressed by algorithms and are calculated in the obvious form through known parameters of this differential equation.
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