Nonsingular group actions and stationary S𝛼S random fields

Roy, Parthanil

doi:10.1090/S0002-9939-10-10250-0

Nonsingular group actions and stationary S$\alpha$S random fields
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Proc. Amer. Math. Soc. 138 (2010), 2195-2202 Request permission

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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