On the rate of complete convergence for weighted sums of arrays of random elements

Abstract

Let {Vnk, k ≥ 1, n ≥ 1} be an array of rowwise independent random elements which are stochastically dominated by a random variable X with E|X|α/γ+θ logρ(|X|) < ∞ for some ρ > 0, α > 0, γ > 0, θ > 0 such that θ + α/γ < 2. Let {ank, k ≥ 1, n ≥ 1} be an array of suitable constants. A complete convergence result is obtained for the weighted sums of the form ∑k=1∞ ank Vnk.