Stable Random Fields, Point Processes and Large Deviations

2014/10/20 by Vicky Fasen, Fasen, Vicky, Parthanil Roy +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #37A40 #60G52. Secondary: 60G60 #60G55 #60G70 #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary: 60F10 #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:37A40 #msc:60F10 #msc:60G52. #msc:60G55 #msc:60G60 #msc:60G70

paper · pdf · doi:10.48550/arxiv.1410.5398

arxiv created 2014/10/20 · openalex publication_date 2014/10/20 · arxiv updated 2014/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric stable non-Gaussian discrete-parameter random field using the framework of Hult and Samorodnitsky (2010). Depending on the ergodic theoretic and group theoretic structures of the underlying nonsingular group action, we observe different large deviation behaviours of this point process sequence. We use our results to study the large deviations of various functionals (e.g., partial sum, maxima, etc.) of stationary symmetric stable fields.

Related

• Ergodic Theory, Abelian Groups, and Point Processes Induced by Stable Random Fields
• Stable random fields indexed by finitely generated free groups
• Large deviations for point processes based on stationary sequences with heavy tails
• Nonsingular Group Actions and Stationary S alpha S Random Fields
• Large deviation principle for geometric and topological functionals and associated point processes