On Strong Law of Large Numbers for pairwise independent random variables
Alina Akhmiarova, Alexander Veretennikov
TL;DR
This paper introduces a new version of the Strong Law of Large Numbers applicable to pairwise independent random variables, relaxing the requirement for finite expectation of each variable.
Contribution
It proposes a novel version of the Strong Law of Large Numbers that works under weaker assumptions of finite expectation for pairwise independent variables.
Findings
Law applies to variables with relaxed expectation conditions
Extends classical results to broader classes of variables
Provides theoretical foundation for further research
Abstract
A new version of a Strong Law of Large Numbers is proposed in this note for pairwise independent random variables. The main goal is to relax the assumption on a finite expectation for each term.
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Taxonomy
TopicsProbability and Risk Models · Stochastic processes and statistical mechanics · Stochastic processes and financial applications