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On complete moment convergence for weighted sums of AANA random variables

Haiwu Huang;  Hanjun Zhang;  Qingxia Zhang — 2016

Kybernetika

In this work, a complete moment convergence theorem is obtained for weighted sums of asymptotically almost negatively associated (AANA) random variables without assumption of identical distribution under some mild moment conditions. As an application, the complete convergence theorems for weighted sums of negatively associated (NA) and AANA random variables are obtained. The result not only generalizes the corresponding ones of Sung [13] and Huang et al. [8], but also improves them.

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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