Asymptotic accuracy in estimation of a fractional signal in a small white noise

Abstract

This paper revisits the problem of estimating the fractional Ornstein - Uhlenbeck process observed in a linear channel with white noise of small intensity. We drive the exact asymptotic formulas for the mean square errors of the filtering and interpolation estimators. The asymptotic analysis is based on approximations of the eigenvalues and eigenfunctions of the signal's covariance operator.