On the Parallelism of Extremal Processes and Subordinators

TL;DR

This paper explores the mathematical parallels between extremal processes and subordinators using Feller semigroup theory, providing new insights and a simplified proof of their invariance principle.

Contribution

It introduces a novel perspective linking extremal processes with subordinators through semigroup theory, offering a concise proof of their invariance principle.

Findings

Identifies parallels between extremal processes and subordinators.

Provides a simplified proof of the invariance principle.

Establishes concepts analogous to Laplace exponent and Lévy measure for extremal processes.

Abstract

We study the extremal processes through Feller semigroups theory from which it is possible to observe some parallelism with subordinators. Consequently, we observe that an extremal process possesses concepts analogous to those of Laplace exponent and L\'evy measure of a subordinator. This approach also yields a short proof of the invariance principle of the extremal processes.