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.

翻译：本文回顾了估算在白噪音小的线性信道中观测到的分数 Ornstein - Uhlenbeck 进程的问题。 我们对过滤器和内插估计器的平均平方差差的精确无药可治公式进行驱动。 无药可治分析基于信号常态操作器的伊金值和元元元的近似值。