Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes

被引：20

作者：

Begyn, Arnaud ^{[1
]}

机构：

[1] Lycee Pierre Fermat, F-31000 Toulouse, France

来源：

BERNOULLI | 2007年 / 13卷 / 03期

关键词：

almost sure convergence; central limit theorem; fractional processes; Gaussian processes; generalized quadratic variations;

D O I：

10.3150/07-BEJ5112

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Cohen, Guyon, Perrin and Pontier have given assumptions under which the second-order quadratic variations of a Gaussian process converge almost surely to a deterministic limit. In this paper we present two new convergence results about these variations: the first is a deterministic asymptotic expansion; the second is a central limit theorem. Next we apply these results to identify two-parameter fractional Brownian motion and anisotropic fractional Brownian motion.

引用

页码：712 / 753

页数：42

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