N-max infinite divisibility and N-max stability

TL;DR

This paper establishes conditions for convergence to max infinitely divisible laws, explores max-stable laws, their domains of attraction, and related extremal processes, advancing the theoretical understanding of max-stability in probability.

Contribution

It provides a necessary and sufficient condition for convergence to max infinitely divisible laws and discusses properties of max-stable laws and extremal processes.

Findings

Characterization of convergence to max infinitely divisible laws

Analysis of max-stable laws and their domains of attraction

Discussion of extremal processes associated with max-stability

Abstract

Here we give a necessary and sufficient condition for the convergence to a random max infinitely divisible law from that of a random maximum. We then discuss random max-stable laws, their domain of max-attraction and the associated extremal processes.