Berry-Esseen bound for the Parameter Estimation of Fractional Ornstein-Uhlenbeck Processes

TL;DR

This paper establishes a Berry-Esseen bound for the least squares estimator of the drift parameter in fractional Ornstein-Uhlenbeck processes driven by fractional Brownian motion with Hurst index between 0.5 and 0.75, using Malliavin calculus.

Contribution

It provides the first Berry-Esseen bound for the parameter estimator in fractional Ornstein-Uhlenbeck processes within this Hurst index range.

Findings

Derived explicit Berry-Esseen bounds for the estimator.

Extended the application of Malliavin calculus to fractional processes.

Improved understanding of the estimator's convergence rate.

Abstract

For an Ornstein-Uhlenbeck process driven by fractional Brownian motion with Hurst index $H\in [\frac12,\frac34]$, we show the Berry-Ess\'een bound of the least squares estimator of the drift parameter. We use an approach based on Malliavin calculus given by Kim and Park \cite{kim 3}.