On the Association of Sum- and Max- Stable Processes

TL;DR

This paper explores the relationship between sum- and max-stable processes through isometries, establishing a natural association that links their structural and classification properties.

Contribution

It introduces a novel framework using linear and max-linear isometries on the extended positive ratio space to connect sum- and max-stable processes.

Findings

Identification of isometries on the extended positive ratio space

Establishment of a natural association between sum- and max-stable processes

Connections between structural and classification results for these processes

Abstract

We address the notion of association of sum- and max- stable processes from the perspective of linear and max-linear isometries. We establish the appealing results that these two classes of isometries can be identified on a proper space (the extended positive ratio space). This yields a natural way to associate to any max-stable process a sum-stable process. By using this association, we establish connections between structural and classification results for sum- and max- stable processes.