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The problem of estimating the fractional Ornstein—Uhlenbeck process observed in a linear channel with white noise of small intensity is considered. Exact asymptotic formulas of the error of the filtering and interpolation estimates are obtained. The accuracy analysis is based on approximations of the eigenvalues and eigenfunctions of the signal’s covariance operator.

Asymptotic Accuracy in Estimation of a Fractional Signal in a Small White Noise