Extremal Value Theory for Long Range Dependent Stable Random Fields

TL;DR

This paper investigates the extreme values of long-range dependent symmetric stable random fields, establishing new types of extremal limit theorems with some limits exhibiting Fréchet distributions.

Contribution

It introduces novel extremal limit theorems for stable random fields with long-range dependence, expanding the understanding of their extreme value behavior.

Findings

New extremal limit theorems in sup measure and cadlag function spaces

Identification of conditions where limits have Fréchet distribution

Characterization of limits for different parameter ranges

Abstract

We study the extremes for a class of a symmetric stable random fields with long range dependence. We prove functional extremal theorems both in the space of sup measures and in the space of cadlag functions of several variables. The limits in both types of theorems are of a new kind, and only in a certain range of parameters these limits have the Fr\'{e}chet distribution.