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

Yong Chen; Nenghui Kuang

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arXiv · 1810.02177

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

Yong Chen·Nenghui Kuang

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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

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Yong Chen, Nenghui Kuang. 2018-10-04. Berry-Ess\'een bound for the Parameter Estimation of Fractional Ornstein-Uhlenbeck Processes with the Hurst Parameter $H\in (0,1/2)$. https://arxiv.org/abs/1810.02177

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