高斯序列二次变分极限定理的充要条件

IF 1.3 Q2 STATISTICS & PROBABILITY Probability Surveys Pub Date : 2019-01-01 DOI:10.1214/15-PS267

L. Viitasaari

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引用次数: 12

摘要

高斯过程的二次变分在随机分析和模型参数估计等应用中都起着重要的作用，因此，该主题在文献中得到了广泛的研究。本文研究了一般高斯序列的二次和的收敛性。给出了各种收敛类型的充分必要条件，包括概率收敛、几乎肯定收敛、$L^{p}$-收敛和弱收敛。我们采用了一种实用而简单的方法，大大简化了现有的方法。作为一个应用，我们展示了如何通过适当选择基础序列来获得给定过程的二次变分的收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Necessary and sufficient conditions for limit theorems for quadratic variations of Gaussian sequences

The quadratic variation of Gaussian processes plays an important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this article we study the convergence of quadratic sums of general Gaussian sequences. We provide necessary and sufficient conditions for different types of convergence including convergence in probability, almost sure convergence, $L^{p}$-convergence as well as weak convergence. We use a practical and simple approach which simplifies the existing methodology considerably. As an application, we show how convergence of the quadratic variation of a given process can be obtained by an appropriate choice of the underlying sequence.

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