Industrial Automatic Control Systems and Controllers Annotation << Back Stochastic Recovery Of Square Integrable Functions S.A. Bulgakov The paper deals with the problem of stochastic recovery of smooth functions on the real line square integrable with respect to the Lebesgue measure from observations of them with additive Gaussian white Gaussian noise. This is a problem of nonparametric (infinite-dimensional) estimation. The procedure of optimal (in the mean square sense) recovery is justified. Conditions for the recovered function to be unbiased and consistent are established. Moreover, a recovery procedure for smooth square integrable functions is proposed and justified, and this procedure provides the best possible estimate (in the order of magnitude) of the number of orthogonal functions depending on the number of observations. Keywords: Orthogonal functions, Fourier coefficients, observation errors, projection estimate, unbiasedness of the recovered function, consistency of the recovered function. DOI: 10.25791/asu.9.2022.1385 Pp. 25-32.