• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.341-349
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• 2003

Let {$x_{nk}\;$\mid$1\;\leq\;k\;\leq\;n,\;n\;\geq\;1$} be an array of random varianbles and $\{a_n$\mid$n\;\geq\;1\}\;and\;\{b_n$\mid$n\;\geq\;1} be a sequence of constants with $a_n\;>\;0,\;b_n\;>\;0,\;n\;\geq\;1. In this paper, for array of row negatively associated(NA) random variables, we establish a general weak law of large numbers (WLLA) of the form (${\sum_{\kappa=1}}^n\;a_{\kappa}X_{n\kappa}\;-\;\nu_{n\kappa})\;/b_n$ converges in probability to zero, as $n\;\rightarrow\;\infty$, where {$\nu_{n\kappa}$\mid$1\;\leq\;\kappa\;\leq\;n,\;n\;\geq\;1$} is a suitable array of constants.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.543-549
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• 2006

Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array $\{X_{{ni},\;u_n{\leq}i{\leq}v_n,\;n{\leq}1\}$ of random variables under a Cesaro type condition, where $\{u_n{\geq}-{\infty},\;n{\geq}1\}$ and $\{v_n{\leq}+{\infty},\;n{\geq}1\}$ large two sequences of integers. In this paper, we extend the result of Sung et al. [13] to a martingale type p Banach space.

• 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

• Journal of the Korean Mathematical Society
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• v.31 no.2
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• pp.279-288
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• 1994

• The Mathematical Education
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• v.21 no.3
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• pp.49-51
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• 1983

• Journal of the Korean Statistical Society
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• v.31 no.3
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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.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.407-415
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• 2011

We establish strong laws of large numbers for weighted sums of arrays of negatively associated random variables under the condition of h-integrability and suitable conditions on the array of weights.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.511-526
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• 2002

In this paper, we concern with SLLN for sums Of in-dependent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and strongly tight random fuzzy sets is obtained.

• 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.22 no.2
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• pp.315-321
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• 2007

We show an exponential inequality for negatively associated and strictly stationary random variables replacing an uniform boundedness assumption by the existence of Laplace transforms. To obtain this result we use a truncation technique together with a block decomposition of the sums. We also identify a convergence rate for the strong law of large number.