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