Regularly Varying Random Fields

TL;DR

This paper investigates the extremal behavior of multivariate regularly varying random fields, introducing new tools like the tail and spectral fields to analyze extremal clusters and applying these methods to Brown-Resnick fields.

Contribution

It extends the theory of tail and spectral processes to multivariate random fields and clarifies multiple notions of extremal index in spatial contexts.

Findings

Introduction of tail and spectral fields for multivariate random fields

Clarification of extremal index notions in spatial settings

Application to Brown-Resnick random fields

Abstract

We study the extremes of multivariate regularly varying random fields. The crucial tools in our study are the tail field and the spectral field, notions that extend the tail and spectral processes of Basrak and Segers (2009). The spatial context requires multiple notions of extremal index, and the tail and spectral fields are applied to clarify these notions and other aspects of extremal clusters. An important application of the techniques we develop is to the Brown-Resnick random fields.