In this paper, we consider the Ornstein–Uhlenbeck (OU) process defined as solution to the equation $d{X}_t=-𝜃X_{t}dt+d{G}_t$, $X_0=0$, where $\{G_t,t\ge 0\}$ is a Gaussian process with stationary increments, whereas $𝜃>0$ is unknown parameter to be estimated. We provide an upper bound in Kolmogorov distance for normal approximation of the least squares estimator ${\widetilde{𝜃}}_T$ of the drift parameter $𝜃$ on the basis of the continuous observation $\{X_t,t\in [0,T]\}$, as $T\to \infty$. Our approach is based on some novel estimates involving a combination of Malliavin calculus and Stein’s method for normal approximation. We apply our result to fractional OU processes of the first kind, and improved the upper bound of the Kolmogorov distance for the LSE ${\widetilde{𝜃}}_T$ provided by [Y. Chen, N. Kuang and Y. Li, Berry–Esseen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes, Stoch. Dyn. 20(4) (2020) 2050023; Y. Chen and Y. Li, Berry–Esseen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes with the hurst parameter $H\in (0,\frac{1}{2})$, Commun. Stat. Theory Methods 50(13) (2021) 2996–3013], respectively, in the cases $H\in (0,\frac{1}{2})$ and $H\in [\frac{1}{2},\frac{3}{4})$. We also apply our approach to fractional OU processes of the second kind.

在本文中，我们考虑将 Ornstein–Uhlenbeck (OU) 过程定义为方程的解$d{X}_t=-𝜃X_{t}dt+d{G}_t$,$X_0=0$， 在哪里$\{G_t,t\ge 0\}$是一个具有平稳增量的高斯过程，而$𝜃>0$是待估计的未知参数。我们为最小二乘估计量的正态逼近提供了柯尔莫哥洛夫距离的上限${\widetilde{𝜃}}_{\mathrm{时间}}$漂移参数$𝜃$在不断观察的基础上$\{X_t,t\epsilon [0,\mathrm{时间}]\}$， 作为$\mathrm{时间}\to \mathrm{无穷大}$。我们的方法基于一些新颖的估计，涉及马利亚文微积分和斯坦因法的正态近似方法的组合。我们将结果应用于第一类分数 OU 过程，并改进了 LSE 的 Kolmogorov 距离的上限${\widetilde{𝜃}}_{\mathrm{时间}}$由[Y. Chen、N. Kuang 和 Y. Li，Berry-Esseen 用于分数 Ornstein-Uhlenbeck 过程的参数估计，Stoch。动态。 20（4）（2020）2050023；Y. Chen 和 Y. Li，Berry-Esseen 用于使用 hurst 参数进行分数 Ornstein-Uhlenbeck 过程的参数估计$H\epsilon （0,\frac{1}{2}）$，交流。统计。理论方法 50 (13)(2021)2996–3013]分别在案例中$H\epsilon （0,\frac{1}{2}）$和$H\epsilon [\frac{1}{2},\frac{3}{4}）$。我们还将我们的方法应用于第二类部分 OU 流程。