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

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...

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Bibliographic Details
Published inModern Stochastics: Theory and Applications Vol. 8; no. 3; pp. 329 - 347
Main Authors Baldé, Maoudo Faramba, Es-Sebaiy, Khalifa
Format Journal Article
LanguageEnglish
Published VTeX 01.09.2021
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Summary: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.
ISSN:2351-6046
2351-6054
DOI:10.15559/21-VMSTA179