• 대한수학회논문집
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• 제13권4호
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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.

• 대한수학회보
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• 제38권1호
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• pp.55-63
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• 2001

In this paper, we derive a general strong law of large numbers and a general weak law of large number for normed weighted sums of pairwise negative quadrant dependent random variables with the common distribution function.

• 대한수학회보
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• 제35권4호
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• pp.769-775
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• 1998

In this paper, we obtain an analogue of law of the iterated logarithm for an array of independent, but not necessarily idetically distributed, random variables under some moment conditions of the array.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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• pp.49-54
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• 2002

For arbitrary random variables {$X_{n},n{\geq}1$}, the order of growth of the series. $S_{n}\;=\;{\sum}_{j=1}^n\;X_{j}$ is studied in this paper. More specifically, when the series S_{n}$ diverges almost surely, the strong law of large numbers $S_{n}/g_{n}^{-1}$($A_{n}{\psi}(A_{n}))\;{\rightarrow}\;0$ a.s. is constructed by extending the results of Petrov (1973). On the other hand, if the series $S_{n}$ converges almost surely to a random variable S, then the tail series $T_{n}\;=\;S\;-\;S_{n-1}\;=\;{\sum}_{j=n}^{\infty}\;X_{j}$ is a well-defined sequence of random variables and converges to 0 almost surely. For the almost surely convergent series $S_{n}$, a tail series strong law of large numbers $T_{n}/g_{n}^{-1}(B_{n}{\psi}^{\ast}(B_{n}^{-1}))\;{\rightarrow}\;0$ a.s., which generalizes the result of Klesov (1984), is also established by investigating the duality between the limiting behavior of partial sums and that of tail series. In particular, an example is provided showing that the current work can prevail despite the fact that previous tail series strong law of large numbers does not work.

• 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.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.419-427
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• 2004

In this paper we establish the Hajeck-Renyi type inequality and derive the strong law of large numbers for asymptotically quadrant sub-independent random variables.

• 충청수학회지
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• 제23권4호
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• pp.835-844
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• 2010

In this paper we study the $H{\grave{a}}jeck-R{\grave{e}}nyi$ type inequality and strong law of large numbers for asymptotically quadrant sub-independent(AQSI) sequences. We also prove the integrability of supremum for AQSI sequences.

• 대한수학회보
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• 제38권3호
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• pp.605-610
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• 2001

It is shown that for each 1 < p < 2 there exist identically distributed uncorrelated random variables $X_n\; with\;E({$\mid$X_1$\mid$}^p)\;<\;{\infty}$, not fulfilling the weak law of large numbers (WLLN). If, however, the random variables are moreover non-negative, the weaker integrability condition $E(X_1\;log\;X_1)\;<\;{\infty}$ already guarantees the strong law of large numbers.

• 대한수학회논문집
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• 제20권1호
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• pp.161-168
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• 2005

In this paper, we obtain strong law of large numbers for linear process generated by asymptotically linear negative quadrant dependence processes.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1997년도 추계학술대회 학술발표 논문집
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• pp.207-213
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• 1997

In this paper, we generalize Kolmogorov' strong law of large numbers to the the case of independent fuzzy random variables.