论文标题
CLT用于高斯过程的二次变化及其在Orey指数估计中的应用
CLT for quadratic variation of Gaussian processes and its application to the estimation of the Orey index
论文作者
论文摘要
我们为$ [0，t] $的二阶二次二次变化给出了二维中央限制定理（CLT）。尽管我们使用的方法在文献中是众所周知的，但CLT所持的条件通常基于相应的协方差函数的不同性。在我们的情况下，我们通过二阶矩的缩放总和的收敛来代替可不同的条件。为了说明该方法的使用的有用性和易用性，我们将获得的CLT应用于证明亚元素布朗运动的Orey指数的估计量的渐近正态性。
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.
