Complete convergence theorem for stationary heavy tailed sequences

TL;DR

This paper establishes a complete convergence theorem for stationary heavy-tailed sequences, providing a foundation for analyzing their extreme value behavior and related processes.

Contribution

It introduces a complete convergence result for space-time point processes of stationary heavy-tailed sequences, with a simplified proof of the invariance principle for partial maximum processes.

Findings

Proves complete convergence for space-time point processes

Provides a simplified proof of the invariance principle

Enhances understanding of extreme value behavior in heavy-tailed sequences

Abstract

For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof of the invariance principle for the corresponding partial maximum process.