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Some limit theorems for m -pairwise negative quadrant dependent random variables

Yongfeng Wu;  Jiangyan Peng — 2018

Kybernetika

The authors first establish the Marcinkiewicz-Zygmund inequalities with exponent p ( 1 ≤ p ≤ 2 ) for m -pairwise negatively quadrant dependent ( m -PNQD) random variables. By means of the inequalities, the authors obtain some limit theorems for arrays of rowwise m -PNQD random variables, which extend and improve the corresponding results in [Y. Meng and Z. Lin (2009)] and [H. S. Sung (2013)]. It is worthy to point out that the open problem of [H. S. Sung, S. Lisawadi, and A. Volodin (2008)] can be solved easily...

Further study on complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated random variables

Haiwu Huang;  Hanjun Zhang;  Qingxia Zhang;  Jiangyan Peng — 2015

Kybernetika

In this paper, the authors further studied the complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated (AANA) random variables with non-identical distribution under some mild moment conditions. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of AANA random variables is obtained. The results not only generalize the corresponding ones of Wang et al. [19], but also partially improve the corresponding ones...

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