Modern Stochastics: Theory and Applications

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.