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.
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页码：94 / 99
页数：6
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