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

TL;DR

This paper derives precise asymptotic formulas for the mean square errors in estimating a fractional Ornstein-Uhlenbeck process observed in small white noise, advancing understanding of filtering accuracy in such stochastic models.

Contribution

It provides exact asymptotic formulas for filtering and interpolation errors in fractional Ornstein-Uhlenbeck processes with small noise, based on eigenvalue and eigenfunction approximations.

Findings

Derived asymptotic formulas for mean square errors

Analyzed eigenvalues and eigenfunctions of the covariance operator

Enhanced understanding of estimation accuracy in fractional processes

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.