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 $\{X_{n,k},1⩽k⩽n,n⩾1\}$ of row-wise extended negatively dependent random variables weakly mean dominated by a random variable $X\in {\mathcal{L}}_1$ and sequences $\{b_n\}$ of positive constants, conditions are given to ensure ${\sum }_{k=1}^n\left(X_{n,k}-\mathbb{E}{X}_{n,k}\right)/b_n\stackrel{\text{a.s.}}{⟶}0$. Our statements also allow us to improve recent results about complete convergence.

15 pages