# Strong laws of large numbers for arrays of row-wise extended negatively dependent random variables

## TL;DR

This paper establishes strong laws of large numbers for arrays of dependent random variables, extending classical results to more general dependence structures and providing conditions for almost sure convergence of normalized sums.

## Contribution

It introduces new strong law results for arrays of extended negatively dependent variables under weak mean domination, improving upon existing convergence theorems.

## Key findings

- Proves almost sure convergence of normalized sums for dependent arrays.
- Provides conditions under which weak mean domination ensures strong laws.
- Enhances previous results on complete convergence for dependent variables.

## Abstract

The main purpose of this paper is to obtain strong laws of large numbers for arrays or weighted sums of random variables under a scenario of dependence. Namely, for triangular arrays $\{X_{n,k}, \, 1 \leqslant k \leqslant n, \, n \geqslant 1 \}$ of row-wise extended negatively dependent random variables weakly mean dominated by a random variable $X \in \mathscr{L}_{1}$ and sequences $\{b_{n} \}$ of positive constants, conditions are given to ensure $\sum_{k=1}^{n} \left(X_{n,k} - \mathbb{E} \, X_{n,k} \right)/b_{n} \overset{\textnormal{a.s.}}{\longrightarrow} 0$. Our statements also allow us to improve recent results about complete convergence.