Nonsingular Group Actions and Stationary S alpha S Random Fields

2009/10/12 by Parthanil Roy, Roy, Parthanil
Computer Science · Mathematics · #37A40. #60G52 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 60G60 #Probability (math.PR) #Secondary 60G70 #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis #math.DS #math.PR #msc:37A40. #msc:60G52 #msc:60G60 #msc:60G70

paper · pdf · doi:10.48550/arxiv.0910.2186

arxiv created 2009/10/12 · openalex publication_date 2009/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with measurable stationary symmetric stable random fields indexed by R^d and their relationship with the ergodic theory of nonsingular R^d-actions. Based on the phenomenal work of Rosinski(2000), we establish extensions of some structure results of stationary S alpha S processes to SαS 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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