Modern Stochastics: Theory and Applications

Keywords: Sub-fractional Ornstein–Uhlenbeck process of second kind

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

Maoudo Faramba Baldé Khalifa Es-Sebaiy

https://doi.org/10.15559/21-VMSTA179

Pub. online: 20 May 2021 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 8, Issue 3 (2021), pp. 329–347

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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