Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kind

• Published in: Modern Stochastics: Theory and Applications Vol. 8; no. 3; pp. 329 - 347
• Main Authors: Baldé, Maoudo Faramba, Es-Sebaiy, Khalifa
• Format: Journal Article
• Language: English
• Published: VTeX 01.09.2021
• Subjects: Berry–Esséen bound; least squares estimator; Malliavin–Stein approach for normal approximations; Sub-fractional Ornstein–Uhlenbeck process of second kind
• ISSN: 2351-6046; 2351-6054
• DOI: 10.15559/21-VMSTA179

In this paper, we deal with an Ornstein–Uhlenbeck process driven by sub-fractional Brownian motion of the second kind with Hurst index $H\in (\frac{1}{2},1)$. We provide a least squares estimator (LSE) of the drift parameter based on continuous-time observations. The strong consistency and the upper bound $O(1/\sqrt{n})$ in Kolmogorov distance for central limit theorem of the LSE are obtained. We use a Malliavin–Stein approach for normal approximations.