A general strong law of large numbers and applications to associated sequences and to extreme value theory

TL;DR

This paper develops a broad strong law of large numbers for arbitrary sequences of random variables using the squared index method, with applications to associated sequences and extreme value theory, offering new insights and comparisons to existing inequalities.

Contribution

It introduces a general SLLN based on the squared index method, extending previous results and applying to associated sequences and EVT with novel examples.

Findings

Established a general SLLN for arbitrary sequences

Provided applications to associated sequences and EVT

Compared with H"ajek-R"enyi type inequalities

Abstract

The purpose of this paper is to establish a general strong law of large numbers (SLLN) for arbitrary sequences of random variables (rv's) based on the squared indice method and to provide applications to SLLN of associated sequences. This SLLN is compared to those based on the H\'ajek-R\'enyi type inequality. Nontrivial examples are given. An interesting issue that is related to extreme value theory (EVT) is handled here.