A central limit theorem for Lipschitz-Killing curvatures of Gaussian excursions

被引：14

作者：

Mueller, Dennis ^{[1
]}

机构：

[1] Karlsruhe Inst Technol, Dept Math, D-76131 Karlsruhe, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 452卷 / 02期

关键词：

Gaussian random field; Excursion set; Lipschitz-Killing curvature; Central limit theorem; Malliavin-Stein method; Wiener chaos expansion; FUNCTIONALS; EXPANSIONS; POINTS; FIELDS;

D O I：

10.1016/j.jmaa.2017.03.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the excursion set of a real stationary isotropic Gaussian random field above a fixed level. We show that the standardized Lipschitz-Killing curvatures of the intersection of the excursion set with a window converges in distribution to a normal distribution as the window grows to the d-dimensional Euclidean space. Moreover a lower bound for the asymptotic variance is derived. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：1040 / 1081

页数：42

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