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On complete moment convergence for weighted sums of negatively superadditive dependent random variables

Haiwu Huang;  Xuewen Lu — 2020

Applications of Mathematics

In this work, the complete moment convergence and complete convergence for weighted sums of negatively superadditive dependent (NSD) random variables are studied, and some equivalent conditions of these strong convergences are established. These main results generalize and improve the corresponding theorems of Baum and Katz (1965) and Chow (1988) to weighted sums of NSD random variables without the assumption of identical distribution. As an application, a Marcinkiewicz-Zygmund-type strong law of...

Convergence of the tail probability for weighted sums of negatively orthant dependent random variables

Haiwu Huang;  Linyan Li;  Xuewen Lu — 2020

Kybernetika

In this research, strong convergence properties of the tail probability for weighted sums of negatively orthant dependent random variables are discussed. Some sharp theorems for weighted sums of arrays of rowwise negatively orthant dependent random variables are established. These results not only extend the corresponding ones of Cai [4], Wang et al. [19] and Shen [13], but also improve them, respectively.

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