• Honam Mathematical Journal
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• v.29 no.3
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• pp.367-375
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• 2007

For bounded negatively associated random variables we derive almost sure convergence and specify the associated rate of convergence by establishing exponential inequality.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.419-425
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• 1996

Let ${X, X_n, n \geq 1}$ be a sequence of independent and identically distributed(i.i.d) random variables with EX = 0 and $E$\mid$X$\mid$^p < \infty$ for some $p \geq 1$. Let ${a_{ni}, 1 \leq i \leq n, n \geq 1}$ be a triangular arrary of constants. The almost sure(a.s) convergence of weighted sums $\sum_{i=1}^{n} a_{ni}X_i$ can be founded in Choi and Sung[1], Chow[2], Chow and Lai[3], Li et al. [4], Stout[6], Sung[8], Teicher[9], and Thrum[10].

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.37-49
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• 1999

We derive the almost sure convergence for weighted sums of random variables which are either pairwise positive quadrant dependent or pairwise positive quadrant dependent or pairwise negative quadrant dependent and then apply this result to obtain the almost sure convergence of weighted averages. e also extend some results on the strong law of large numbers for pairwise independent identically distributed random variables established in Petrov to the weighted sums of pairwise negative quadrant dependent random variables.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.797-804
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• 1999

In this paper we derive the almost sure convergence of weighted sums of 2-dimensional arrays of random variables which are either pairwise positive quadrant dependent or associated. Our re-sults imply and extension of Etemadi's(1983) strong laws of large numbers for weighted sums of nonnegative random variables to the 2-dimensional case.

• Communications for Statistical Applications and Methods
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• v.16 no.6
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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.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.191-204
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• 2022

This paper introduces the statistical convergence concepts of double sequences of complex uncertain variables: statistical convergence almost surely(a.s.), statistical convergence in measure, statistical convergence in mean, statistical convergence in distribution and statistical convergence uniformly almost surely(u.a.s.).

• Honam Mathematical Journal
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• v.34 no.2
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• pp.241-252
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• 2012

Let $\{X_{ni},\;1{\leq}i{\leq}n,\;n{\geq}1\}$ be a sequence of LNQD which are dominated randomly by another random variable X. We obtain the complete convergence and almost sure convergence of weighted sums ${\sum}^n_{i=1}a_{ni}X_{ni}$ for LNQD by using a new exponential inequality, where $\{a_{ni},\;1{\leq}i{\leq}n,\;n{\geq}1\}$ is an array of constants. As corollary, the results of some authors are extended from i.i.d. case to not necessarily identically LNQD case.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.57-67
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• 1997

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.137-143
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• 2007

In this paper, a Berstein-Hoeffding type inequality is established for linearly negative quadrant dependent random variables. A condition is given for almost sure convergence and the associated rate of convergence is specified.