Strong laws for weighted sums of random variables satisfying generalized Rosenthal type inequalities

Abstract

Let 1 ≤ p < 2 and 0 < α, β < ∞ with 1/p = 1/α + 1/β. Let {X n , n ≥ 1} be a sequence of random variables satisfying a generalized Rosenthal type inequality and stochastically dominated by a random variable X with E|X| β < ∞. Let {a nk , 1 ≤ k ≤ n, n ≥ 1} be an array of constants satisfying n k=1 |a nk | α = O(n). Marcinkiewicz-Zygmund type strong laws for weighted sums of the random variables are established. Our results generalize or improve the corresponding ones of Wu (