Stationary symmetric α-stable discrete parameter random fields

被引：27

作者：

Roy, Parthanil ^{[1
]}

Samorodnitsky, Gennady ^{[1
]}

机构：

[1] Cornell Univ, Sch Operat Res & Ind Engn, Ithaca, NY 14853 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2008年 / 21卷 / 01期

基金：

美国国家科学基金会;

关键词：

random field; stable process; ergodic theory; maxima; extreme value theory; group action; non-singular map; dissipative; conservative;

D O I：

10.1007/s10959-007-0107-9

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 establish a connection between the structure of a stationary symmetric alpha-stable random field (0 < alpha < 2) and ergodic theory of non-singular group actions, elaborating on a previous work by Rosinski (Ann. Probab. 28:1797-1813, 2000). With the help of this connection, we study the extreme values of the field over increasing boxes. Depending on the ergodic theoretical and group theoretical structures of the underlying action, we observe different kinds of asymptotic behavior of this sequence of extreme values.

引用

页码：212 / 233

页数：22

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