• 호남수학학술지
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• 제26권3호
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• pp.287-298
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• 2004

In this paper we derive complete convergences for weighted sums of asymptotically almost negatively associated random variables.

• 호남수학학술지
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• 제32권1호
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• pp.91-99
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• 2010

In this paper we introduce the concept of asymptotically almost negatively associated random variables in a Hilbert space and obtain the strong law of large numbers for a strictly stationary asymptotically almost negatively associated sequence of H-valued random variables with zero means and finite second moments. As an application we prove a strong law of large numbers for a linear process generated by asymptotically almost negatively random variables in a Hilbert space with this result.

• 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.

• Communications for Statistical Applications and Methods
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• 제16권6호
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• pp.1013-1022
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• 2009

We in this paper study the almost sure convergence for asymptotically almost negatively associated(AANA) random variable sequences and obtain some new results which extend and improve the result of Jamison et al. (1965) and Marcinkiewicz-Zygumnd strong law types in the form given by Baum and Katz (1965), three-series theorem.

• 충청수학회지
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• 제26권1호
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• pp.137-145
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• 2013

In this paper we obtain the complete convergence of weighted sums of asymptotically almost negatively associated random variables. Some previous known results for negatively associated random variables are generalized to asymptotically almost negative association case.

• 대한수학회논문집
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• 제26권1호
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• pp.151-161
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• 2011

Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.209-213
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• 2002

We study maximal second moment inequality and derive complete convergence for weighted sums of asymptotically almost negatively associated(AANA) random variables by applying this inequality. 2000 Mathematics Subject Classification : 60F05

• 대한수학회논문집
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• 제18권3호
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• pp.551-558
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• 2003

In this paper we Obtain the Hajeck-Renyi type inequality for the asymptotically almost negatively associated(AANA) random variables and extend some results for negatively associated random variables to the AANA case by applying this inequality.

• Journal of the Korean Statistical Society
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• 제31권3호
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• pp.369-378
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• 2002

Strong laws of large numbers for weighted sums of asymptotically almost negatively associated(AANA) sequence are proved by our generalized maximal inequality for AANA random variables at a crucial step.

• 대한수학회보
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• 제43권1호
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• pp.169-178
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• 2006

For double arrays of constants ${a_{ni},\;1{\leq}i{\leq}k_n,\;n{\geq}1}$ and sequences ${X_n,\;n{\geq}1}$ of asymptotically almost negatively associated (AANA) random variables the almost sure convergence of $\sum\limits{_{i=1}}{^{k_n}}\;a_{ni}X_i$ is derived.