The complete convergence for pairwise negative quadrant dependent PNQD random variables is studied. So far there has not been the generalmoment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. ...

Let {Xni, i ≥ 1, n ≥ 1} be an array of rowwise asymptotically almost negatively associated random variables. Some sufficient conditions for complete convergence for arrays of rowwise asymptotically almost negatively associated random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted s...

For double arrays of constants {ani, 1 ≤ i ≤ kn, n ≥ 1} and sequences of negatively orthant dependent random variables {Xn, n ≥ 1}, the conditions for strong law of large number of ∑kn i=1 aniXi are given. Both cases kn ↑ ∞ and kn = ∞ are treated.

A sequence of random variables is said to be extended negatively dependent (END) if the tails of its finite-dimensional distributions in the lower-left and upper-right corners are dominated by a multiple of the tails of the corresponding finite-dimensional distributions of a sequence of independent random variables with the samemarginal distributions. The goal of this paper is to establish the ...

In this article, some strong convergence results for weighted sums of negatively superadditive dependent random variables are studied without assumption of identical distribution. The results not only generalize the corresponding ones of Cai (Metrika 68:323-331, 2008) and Sung (Stat. Pap. 52:447-454, 2011), but also extend and improve the corresponding one of Chen and Sung (Stat. Probab. Lett. ...

We discuss sufficient conditions that guarantee the existence of asymptotic expansions for Central Limit Theorem weakly dependent random variables including observations arising from sufficiently chaotic dynamical systems like piece-wise expanding maps, and strongly ergodic Markov chains. primarily use spectral techniques to obtain results.