  The paper concerns problems of the recovery of linear operators defined on
sets of functions from information of these functions given with stochastic
errors. The constructed optimal recovery methods, in general, do not use all
the available information. As a consequence, optimal methods are obtained for
recovering derivatives of functions from Sobolev classes by the information of
their Fourier transforms given with stochastic errors. A similar problem is
considered for solutions of the heat equation.
