Equivalent conditions of complete moment convergence and complete integral convergence for NOD sequences
Bull. Korean Math. Soc. 2017 Vol. 54, No. 3, 917-933
https://doi.org/10.4134/BKMS.b160357
Published online May 31, 2017
Xin Deng and Xuejun Wang
Anhui University, Anhui University
Abstract : 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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