Nonsingular group actions and stationary SS random fields

Author:
Parthanil Roy

Journal:
Proc. Amer. Math. Soc. **138** (2010), 2195-2202

MSC (2010):
Primary 60G60; Secondary 60G70, 60G52, 37A40

DOI:
https://doi.org/10.1090/S0002-9939-10-10250-0

Published electronically:
February 2, 2010

MathSciNet review:
2596059

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper deals with measurable stationary symmetric stable random fields indexed by and their relationship with the ergodic theory of nonsingular -actions. Based on the phenomenal work of Rosiński (2000), we establish extensions of some structure results of stationary processes to fields. Depending on the ergodic theoretical nature of the underlying action, we observe different behaviors of the extremes of the field.

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Preprint, available at http://arxiv.org/abs/0712.0688.

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Preprint.

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Additional Information

**Parthanil Roy**

Affiliation:
Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824-1027

Email:
roy@stt.msu.edu

DOI:
https://doi.org/10.1090/S0002-9939-10-10250-0

Keywords:
Random field,
stable process,
extreme value theory,
maxima,
ergodic theory,
nonsingular group action,
dissipative,
conservative

Received by editor(s):
December 30, 2008

Received by editor(s) in revised form:
October 9, 2009

Published electronically:
February 2, 2010

Additional Notes:
The author was supported in part by NSF grant DMS-0303493 and NSF training grant “Graduate and Postdoctoral Training in Probability and Its Applications” at Cornell University, the RiskLab of the Department of Mathematics, ETH Zurich, and a start-up grant from Michigan State University.

Communicated by:
Richard C. Bradley

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.