EXCURSION SETS OF THREE CLASSES OF STABLE RANDOM FIELDS

被引：20

作者：

Adler, Robert J. ^{[1
]}

Samorodnitsky, Gennady ^{[2
]}

Taylor, Jonathan E. ^{[3
]}

机构：

[1] Technion Israel Inst Technol, Fac Elect Engn, IL-32000 Haifa, Israel

[2] Cornell Univ, Ithaca, NY 14853 USA

[3] Stanford Univ, Dept Stat, Stanford, CA 94305 USA

来源：

ADVANCES IN APPLIED PROBABILITY | 2010年 / 42卷 / 02期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

Stable random field; harmonisable field; excursion set; Euler characteristic; intrinsic volume; geometry;

D O I：

10.1239/aap/1275055229

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：

Studying the geometry generated by Gaussian and Gaussian-related random fields via their excursion sets is now a well-developed and well-understood subject. The purely non-Gaussian scenario has, however, not been studied at all. In this paper we look at three classes of stable random fields, and obtain asymptotic formulae for the mean values of various geometric characteristics of their excursion sets over high levels. While the formulae are asymptotic, they contain enough information to show that not only do stable random fields exhibit geometric behaviour very different from that of Gaussian fields, but they also differ significantly among themselves.

引用

页码：293 / 318

页数：26

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[3]

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[4]

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