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Bull. Korean Math. Soc. 2017; 54(3): 917-933
Online first article November 11, 2016 Printed May 31, 2017
https://doi.org/10.4134/BKMS.b160357
Copyright © The Korean Mathematical Society.
Equivalent conditions of complete moment convergence and complete integral convergence for NOD sequences
Xin Deng and Xuejun Wang
Anhui University, Anhui University
In this paper, seven equivalent conditions of complete moment convergence and complete integral convergence for negatively orthant dependent (NOD, in short) sequences are shown under two cases: identical distribution and stochastic domination. The results obtained in the paper improve and generalize the corresponding ones of Liang et al. \cite{10}). In addition, an extension of the Baum-Katz complete convergence theorem: six equivalent conditions of complete convergence is established.
Keywords: complete convergence, complete moment convergence, complete integral convergence, negatively orthant dependent sequence, stochastic domination
MSC numbers: 60F15, 60G50
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