• 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.

• 충청수학회지
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• 제28권3호
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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 applied mathematics & informatics
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• 제30권3_4호
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• pp.623-633
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• 2012

Let {${\Omega}$, $\mathcal{F}$, P} be a probability space and {$X_n|n{\geq}1$} be a sequence of random variables defined on it. A finite sequence of random variables {$X_n|n{\geq}1$} is said to be conditionally negatively associated given $\mathcal{F}$ if for every pair of disjoint subsets A and B of {1, 2, ${\cdots}$, n}, $Cov^{\mathcal{F}}(f_1(X_i,i{\in}A),\;f_2(X_j,j{\in}B)){\leq}0$ a.s. whenever $f_1$ and $f_2$ are coordinatewise nondecreasing functions. We extend the H$\grave{a}$jek-R$\grave{e}$nyi-type inequality from negative association to conditional negative association of random variables. In addition, some corollaries are given.

• 호남수학학술지
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• 제36권3호
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• pp.679-688
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• 2014

The notion of asymptotically negative dependence for collection of random variables is generalized to a Hilbert space and the almost sure convergence for these H-valued random variables is obtained. The result is also applied to a linear process generated by H-valued asymptotically negatively dependent random variables.

• 충청수학회지
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• 제32권3호
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• pp.327-336
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• 2019

In this paper, the weak laws of large numbers for sums of asymptotically almost negatively associated random vectors in Hilbert spaces are investigated. Some results in Hien and Thanh ([3]) are generalized to asymptotically almost negatively random vectors in Hilbert space.