Convergence rate of CLT for the drift estimation of sub-fractional Ornstein–Uhlenbeck process of second kind
Volume 8, Issue 3 (2021), pp. 329–347
Pub. online: 20 May 2021
Type: Research Article
Open Access
Open Access
Received
8 October 2020
8 October 2020
Revised
3 March 2021
3 March 2021
Accepted
4 May 2021
4 May 2021
Published
20 May 2021
20 May 2021
Abstract
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.
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