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On complete moment convergence for weighted sums of negatively superadditive dependent random variables. (English) Zbl 07250667
Summary: 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 L. E. Baum and M. Katz [Trans. Am. Math. Soc. 120, 108–123 (1965; Zbl 0142.14802)] and Y. S. Chow [Bull. Inst. Math., Acad. Sin. 16, No. 3, 177–201 (1988; Zbl 0655.60028)] 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.
MSC:
60F15 Strong limit theorems
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