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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nonsingular group actions and stationary S$ \alpha$S random fields


Author: Parthanil Roy
Journal: Proc. Amer. Math. Soc. 138 (2010), 2195-2202
MSC (2010): Primary 60G60; Secondary 60G70, 60G52, 37A40
Published electronically: February 2, 2010
MathSciNet review: 2596059
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Abstract: This paper deals with measurable stationary symmetric stable random fields indexed by $ \mathbb{R}^d$ and their relationship with the ergodic theory of nonsingular $ \mathbb{R}^d$-actions. Based on the phenomenal work of Rosiński (2000), we establish extensions of some structure results of stationary $ S\alpha S$ processes to $ S\alpha S$ 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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Additional Information

Parthanil Roy
Affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824-1027
Email: roy@stt.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10250-0
PII: S 0002-9939(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.