Central limit theorems for the excursion set volumes of weakly dependent random fields

被引：39

作者：

Bulinski, Alexander ^{[1
]}

Spodarev, Evgeny ^{[2
]}

Timmermann, Florian ^{[2
]}

机构：

[1] Moscow MV Lomonosov State Univ, Dept Math & Mech, Moscow 119991, Russia

[2] Univ Ulm, Inst Stochast, D-89069 Ulm, Germany

来源：

BERNOULLI | 2012年 / 18卷 / 01期

关键词：

central limit theorem; dependence conditions; excursion sets; random fields; FUNCTIONALS; VARIABLES; LEVEL;

D O I：

10.3150/10-BEJ339

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：

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on R-d are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the covariance matrix of the limiting distribution are provided. A statistical version of the CLT is considered as well. Some numerical results are also discussed.

引用

页码：100 / 118

页数：19

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