Point processes in a metric space

TL;DR

This paper explores the definition and properties of point processes in metric spaces, emphasizing their role in extreme value theory and heavy-tailed data analysis, and provides a convergence result for iid sequences.

Contribution

It introduces a comprehensive framework for point processes in metric spaces and demonstrates a complete convergence theorem for regularly varying iid sequences.

Findings

Established properties of point processes in metric spaces

Proved a complete convergence result for iid sequences

Enhanced understanding of heavy-tailed data analysis

Abstract

As a useful and elegant tool of extreme value theory, the study of point processes on a metric space is important and necessary for the analyses of heavy-tailed functional data. This paper focuses on the definition and properties of such point processes. A complete convergence result for a regularly varying iid sequence in a metric space is proved as an example of the application in extreme value theory.