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

共 17 条

[1] Adler R. J., 1981, GEOMETRY RANDOM FIEL
[2] [Anonymous], 2003, Contemporary Mathematics
[3] AYACHE A, 2005, P 5 ISSAC C CAT
[4] Baxter G, 1956, P AM MATH SOC, V7, P522
[5] Begyn A., 2005, ELECTRON J PROBAB, V10, P691, DOI DOI 10.1214/EJP.V10-245
[6] BENASSI A, 1997, REV MATH IBOAMERICA, V13, P7
[7] BIERME H, 2006, UNPUB ESTIMATION ANI
[8] BINGHAM H, 1989, REGULAR VARIATION
[9] Anisotropic analysis of some Gaussian models
Bonami, A
Estrade, A
[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2003, 9 (03) : 215 - 236
[10] COEURJOLLY J, 2000, THESIS U GRENOBLE 1

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