• Journal of applied mathematics & informatics
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• v.29 no.5_6
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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.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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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 Institute of Intelligent Systems
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• v.13 no.6
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• pp.754-758
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• 2003

The present paper establishes a strong law of large numbers for sums of tight fuzzy random variables as a generalization of SLLN for sums of independent and identically distributed fuzzy random variables.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.343-351
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• 2011

In this paper, we establish a Marcinkiewicz-Zygmund type strong law for sequences of blockwise and pairwise m-dependent random variables. The sharpness of the results is illustrated by an example.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.151-158
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• 1998

In this note we derive inequalities of linearly positive quadrant dependent random variables and obtain a strong law of large numbers for linealy positive quardant dependent random variables. Our results imply an extension of Birkel's strong law of large numbers for associated random variables to the linear positive quadrant dependence case.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.795-805
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• 2008

The aim of this paper is to extend the "classical degenerate convergence criterion" and the Feller weak law of large numbers to double adapted arrays of random variables.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.385-391
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• 1998

In this note, we study a weak law of large numbers for sequences of exchangeable random variables. As a special case, we have an extension of Kolmogorov's generalization of Khintchine's weak law of large numbers to i.i.d. random variables.

• 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.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.379-392
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• 2013

A general result for the complete convergence of arrays of rowwise extended negatively dependent random variables is derived. As its applications eight corollaries for complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables are given, which extend the corresponding known results for independent case.