Almost sure convergence of weighted sums

Abstract

Let {X,Xn,n≥1} be a sequence of identically distributed random variables and {ai,n,1≤i≤n} be a triangular array of constants. In this short paper, we establish a general almost sure convergence theorem for the weighted sum Sn=∑ni=1ai,nXi. Our results improves the works of Sung [14]. Furthermore, almost sure convergence theorems of Sn for negatively associated random variables, martingale difference sequence and p-mixing sequence are obtained. © 2013 Miskolc University Press.