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 large numbers for weighted sums of NSD random variables is obtained.

中文翻译：

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负超加性相关随机变量加权和的完全矩收敛性

在这项工作中，研究了负超加性因变量（NSD）随机变量的加权和的完全矩收敛和完全收敛，并建立了这些强收敛的一些等价条件。这些主要结果推广了Baum和Katz（1965）以及Chow（1988）的相应定理，并将其改进为NSD随机变量的加权和，而无需假设分布相同。作为应用，获得了NSD随机变量的加权和的Marcinkiewicz-Zygmund型强数定律。