• 대한수학회보
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• 제33권3호
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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].

• 대한수학회지
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• 제36권1호
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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.

• 대한수학회논문집
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• 제14권4호
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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.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1351-1361
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• 2011

We in this paper study the complete convergence and almost surely convergence for arrays of rowwise pairwise negatively dependent(ND) random variables (r.${\upsilon}$.'s) which are dominated randomly by some random variables and obtain a result dealing with complete convergence of linear processes.

• 대한수학회보
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• 제38권4호
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• pp.763-772
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• 2001

The rate of convergence for an almost surely convergent series $S_n={\Sigma^n}_{i-1}X_i$ of independent random variables is studied in this paper. More specifically, when S$_{n}$ converges almost surely to a random variable S, the tail series $T_n{\equiv}$ S - S_{n-1} = {\Sigma^\infty}_{i-n} X_i$ is a well-defined sequence of random variables with T$_{n}$ $\rightarrow$ 0 almost surely. Conditions are provided so that for a given positive sequence {$b_n, n {\geq$ 1}, the limit law sup$_{\kappa}\geqn | T_{\kappa}|/b_n \rightarrow$ 0 holds. This result generalizes a result of Nam and Rosalsky [4].

• 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

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.277-282
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• 2002

In this paper we shall discuss the relationship between almost periodic fuzzy mappings and the properties of convergence theorems, and some results of almost periodic fuzzy mappings.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.91-109
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• 1995

The rate of convergence to a random variable S for an almost certainly convergent series $S_n = \sum^n_{j=1} X_j$ of independent random variables is studied in this paper. More specifically, when $S_n$ converges to S almost certainly, the tail series $T_n = \sum^{\infty}_{j=n} X_j$ is a well-defined sequence of random variable with $T_n \to 0$ a.c. Various sets of conditions are provided so that for a given numerical sequence $0 < b_n = o(1)$, the tail series strong law of large numbers $b^{-1}_n T_n \to 0$ a.c. holds. Moreover, these results are specialized to the case of the weighted i.i.d. random varialbes. Finally, example are provided and an open problem is posed.

• 호남수학학술지
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• 제34권2호
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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.

• 대한수학회논문집
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• 제22권1호
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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.