Stationary Symmetric α-Stable Discrete Parameter Random Fields

被引：0

作者：

Parthanil Roy

Gennady Samorodnitsky

机构：

[1] Cornell University,School of Operations Research and Industrial Engineering

来源：

Journal of Theoretical Probability | 2008年 / 21卷

关键词：

60G60; 37A40; Random field; Stable process; Ergodic theory; Maxima; Extreme value theory; Group action; Non-singular map; Dissipative; Conservative;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We establish a connection between the structure of a stationary symmetric α-stable random field (0<α<2) and ergodic theory of non-singular group actions, elaborating on a previous work by Rosiński (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：21

共 10 条

[1]

De Loera J.(2005)The many aspects of counting lattice points in polytopes Math. Semesterber. 52 175-195

[2]

Hardin C.(1982)On the spectral representation of symmetric stable processes J. Multivar. Anal. 12 385-401

[3]

Maharam D.(1964)Incompressible transformations Fundam. Math. 56 35-50

[4]

Rosiński J.(1995)On the structure of stationary stable processes Ann. Probab. 23 1163-1187

[5]

Rosiński J.(2000)Decomposition of stationary Ann. Probab. 28 1797-1813

[6]

Samorodnitsky G.(2004)-stable random fields Ann. Probab. 32 1438-1468

[7]

Surgailis D.(1993)Extreme value theory, ergodic theory, and the boundary between short memory and long memory for stationary stable processes Probab. Theory Relat. Fields 97 543-558

[8]

Rosiński J.(undefined)Stable mixed moving averages undefined undefined undefined-undefined

[9]

Mandrekar V.(undefined)undefined undefined undefined undefined-undefined

[10]

Cambanis S.(undefined)undefined undefined undefined undefined-undefined

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