Berry-Ess\'een bound for the Parameter Estimation of Fractional Ornstein-Uhlenbeck Processes with the Hurst Parameter $H\in (0,1/2)$

TL;DR

This paper establishes a Berry-Esséen bound for the least squares estimator of the drift parameter in fractional Ornstein-Uhlenbeck processes with Hurst parameter H in (0, 1/2), filling a gap in previous research.

Contribution

It extends the Berry-Esséen bound results to the case H in (0, 1/2), using Malliavin calculus, thus completing the analysis for all H in (0, 3/4).

Findings

Berry-Esséen bound proved for H in (0, 1/2)

Addresses a previously unresolved case in fractional OU processes

Uses Malliavin calculus approach for the proof

Abstract

For an Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst parameter 0<H<1/2, one shows the Berry-Ess\'een bound of the least squares estimator of the drift parameter. Thus, a problem left in the previous paper (Chen, Kuang and Li in Stochastics and Dynamics, 2019+) is solved, where the Berry-Ess\'een bound of the least squares estimator is proved for 1/2<=H<=3/4. An approach based on Malliavin calculus given by Kim and Park \cite{kim 3} is used