Stable random fields, point processes and large deviations

Article Type

Research Article

Publication Title

Stochastic Processes and their Applications

Abstract

We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric α-stable (0<α<2) 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.

First Page

832

Last Page

856

DOI

10.1016/j.spa.2015.09.020

Publication Date

3-1-2016

Comments

Open Access; Green Open Access

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