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

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 Hájek-Rényi type inequality. Nontrivial examples are given. An interesting issue that is related to extreme value theory (EVT) is handled here.