• 대한수학회보
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• 제54권3호
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• pp.917-933
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• 2017

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. [10]). In addition, an extension of the Baum-Katz complete convergence theorem: six equivalent conditions of complete convergence is established.

• 충청수학회지
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• 제29권3호
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• pp.477-489
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• 2016

The purpose of this paper is to establish the complete moment convergence and the integrability of supremum for weighted sums of pairwise negatively quadrant dependent random variables satisfying stochastically dominating condition.

• 대한수학회지
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• 제54권3호
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• pp.877-896
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• 2017

In this paper, the complete convergence and complete moment convergence for a class of random variables satisfying the Rosenthal type inequality are investigated. The sufficient and necessary conditions for the complete convergence and complete moment convergence are provided. As applications, the Baum-Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for a class of random variables satisfying the Rosenthal type inequality are established. The results obtained in the paper extend the corresponding ones for some dependent random variables.

• Journal of applied mathematics & informatics
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• 제37권3_4호
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• pp.207-217
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• 2019

We are presented of several basic properties for negatively superadditive dependent(NSD) random variables. By using this concept we are obtained complete convergence for maximum partial sums of rowwise NSD random variables. These results obtained in this paper generalize a corresponding ones for independent random variables and negatively associated random variables.