• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.45-55
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• 2016

Let {$X_n,n{\geq}1$} be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums ${\frac{1}{g(n)}}{\sum_{i=1}^{n}}{\frac{X_i}{h(i)}}$ of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law of large numbers and Marcinkiewicz-Zygmund strong law of large numbers for negatively superadditive dependent random variables are obtained. Our results generalize the corresponding ones for independent random variables and negatively associated random variables.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.855-863
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• 1998

Some conditions on the strong law of large numbers for weighted sums of negative quadrant dependent random variables are studied. The almost sure convergence of weighted sums of negatively associated random variables is also established, and then it is utilized to obtain strong laws of large numbers for weighted averages of negatively associated random variables.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.75-83
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• 2011

In this paper the Baum-Katz law of large numbers for negatively orthant dependent random variables is studied. The complete convergence of negatively orthant dependent random variables under some conditions of uniform integrablity is also obtained.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.51-68
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• 2020

In this paper, the author considers the nonparametric regression model with negatively orthant dependent random variables. The wavelet procedures are developed to estimate the regression function. For the wavelet estimator of unknown function g(·), the almost sure consistency is derived and the complete consistency is established under the mild conditions. Our results generalize and improve some known ones for independent random variables and dependent random variables.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.379-392
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• 2013

A general result for the complete convergence of arrays of rowwise extended negatively dependent random variables is derived. As its applications eight corollaries for complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables are given, which extend the corresponding known results for independent case.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.325-334
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• 2015

In this paper we obtain complete convergences for weighted sums of negatively superadditive dependent random variables. These results generalize the corresponding ones for negatively associated random variables.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.721-730
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• 2010

In this paper we consider some results on convergence for arrays of rowwise and pairwise negatively quadrant dependent random variables.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.409-417
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• 2015

In this paper, some $L_p$-convergences and complete convergences of the maximum of the partial sum for negatively superadditive dependent random variables are obtained. The proofs of the results are based on a new Rosenthal type inequality concerning negatively superadditive dependent random variables.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.133-146
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• 2020

In this paper, we established the complete moment convergence for sequences of m-pairwise negatively quadrant dependent random variables which are weakly upper bounded by a random variable X.