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Equivalent conditions of complete moment convergence and complete integral convergence for NOD sequences

Xuejun Wang|Xin Deng
대한수학회 (The Korean Mathematical Society)|2017.05|대한수학회보 (Bulletin of the KMS)|제54권 제3호|pp. 917-933

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참고문헌

키워드

complete moment convergencecomplete convergencecomplete integral convergencenegatively orthant dependent sequencestochastic domination
주제분류수학

초록

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.

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.

참고문헌 (28)

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