ABSTRACT: In this paper, the complete convergence and the complete moment convergence of weighted sums for an array of negatively superadditive dependent random variables are established. The results generalize the Baum-Katz theorem on negatively superadditive dependent random variables. In particular, the Marcinkiewicz-Zygmund type strong law of large numbers of weights sums for sequences of n...

Let {Xni} be an array of rowwise independent B-valued random elements and {an} constants such that 0 < an ↑ ∞. Under some moment conditions for the array, it is shown that ∑n i=1Xni/an converges to 0 completely if and only if ∑n i=1Xni/an converges to 0 in probability.

Let {Xnk: k,n 1,2 be an array of row-wise independent random elements in a separable Banach space. Let {ank: k,n 1,2 be an array of Voo voo R+ real numbers such that /-k=l lank -< 1 and Ln=l exp(-a/A < for each c e where n V 2 Voo An kk=l ank. The complete convergence of l’k=l ank Xnk is obtained under varying moment and distribution conditions on the random elements. In particular, laws of lar...

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We give out a general method to prove the complete convergence for arrays of rowwise ρ-mixing random variables and to present some results on complete convergence under some suitable conditions. Some results generalize previous known r...