Number of critical points of a Gaussian random field: Condition for a finite variance

被引：9

作者：

Estrade, Anne ^{[1
]}

Fournier, Julie ^{[1
,2
]}

机构：

[1] Univ Paris 05, CNRS, UMR 8145, MAP5, 45 Rue St Peres, F-75006 Paris, France

[2] Univ Paris 06, F-75252 Paris 05, France

来源：

STATISTICS & PROBABILITY LETTERS | 2016年 / 118卷

关键词：

Gaussian field; Critical point; Geman condition; Crossing; LEVEL-CROSSINGS; MOMENTS; ZEROS;

D O I：

10.1016/j.spl.2016.06.018

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：

We study the number of points where the gradient of a stationary Gaussian random field restricted to a compact set in R-d takes a fixed value. We extend to higher dimensions the Geman condition, a sufficient condition on the covariance function under which the variance of this random variable is finite. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：94 / 99

页数：6

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