We give a two-dimensional central limit theorem (CLT) for the second-order quadratic variation of the centered Gaussian processes on $[0,T]$. Though the approach we use is well known in the literature, the conditions under which the CLT holds are usually based on differentiability of the corresponding covariance function. In our case, we replace differentiability conditions by the convergence of the scaled sums of the second-order moments. To illustrate the usefulness and easiness of use of the approach, we apply the obtained CLT to proving the asymptotic normality of the estimator of the Orey index of a subfractional Brownian motion.

中文翻译：

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用于高斯过程二次变化的 CLT 及其在 Orey 指数估计中的应用

我们给出了 $[0,T]$ 上居中高斯过程的二阶二次变分的二维中心极限定理 (CLT)。尽管我们使用的方法在文献中是众所周知的，但 CLT 成立的条件通常基于相应协方差函数的可微性。在我们的例子中，我们用二阶矩的缩放和的收敛来代替可微性条件。为了说明该方法的有用性和易用性，我们将获得的 CLT 应用于证明亚分数布朗运动的奥雷指数估计量的渐近正态性。