• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.369-383
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• 2010

We obtain a result on complete convergence of weighted sums for arrays of rowwise independent Banach space valued random elements. No assumptions are given on the geometry of the underlying Banach space. The result generalizes the main results of Ahmed et al. [1], Chen et al. [2], and Volodin et al. [14].

• The Journal of Natural Sciences
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• v.13 no.1
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• pp.1-6
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• 2003

Strong laws of large numbers are established for the weighted sums of i.i.d. random variables which have higher order moment condition. One of the results of Sung(2001) is extended.

• Journal of the Korean Statistical Society
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• v.33 no.1
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• pp.99-106
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• 2004

Let {X, $X_{n}, n\;{\geq}\;1$} be a sequence of identically distributed, negatively associated (NA) random variables and assume that $│X│^{r}$, r > 0, has a finite moment generating function. A strong law of large numbers is established for weighted sums of these variables.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.1007-1025
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• 2019

In the present work, the complete convergence and complete moment convergence properties for arrays of rowwise extended negatively dependent (END) random variables are investigated. Some sharp theorems on these strong convergence for weighted sums of END cases are established. These main results not only generalize the known corresponding ones of Cai [2], Wang et al. [17] and Shen [14], but also improve them, respectively.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.457-473
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• 2019

In this paper, we investigate weak laws of large numbers for weighted coordinatewise pairwise negative quadrant dependence random vectors in Hilbert spaces in the case that the decay order of tail probability is r for some 0 < r < 2. Moreover, we extend results concerning Pareto-Zipf distributions and St. Petersburg game.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.137-145
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• 2013

In this paper we obtain the complete convergence of weighted sums of asymptotically almost negatively associated random variables. Some previous known results for negatively associated random variables are generalized to asymptotically almost negative association case.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.883-894
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• 2004

We discuss in this paper the strong convergence for weighted sums of negative associated (in abbreviation: NA) arrays. Meanwhile, the central limit theorem for weighted sums of NA variables and linear process based on NA variables is also considered. As corollary, we get the results on iid of Li et al. ([10]) in NA setting.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.273-285
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• 1999

In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights {$W_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}n{\geq}1$} and on the triangular array of random variables {$X_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}{\geq}1$} which ensure that $\sum_{j=1}^{n}{\;}W_{nj}{\mid}X_{nj}{\;}-{\;}B_{nj}{\mid}$ converges In probability to 0, where {$B_{nj}{\;}:{\;}1{\;}{\leq}{\;}j{\;}{\leq}{\;}n,{\;}n{\;}{\geq}{\;}1$} is a centering array of constants or 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.

• Journal of Applied Reliability
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• v.12 no.4
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• pp.265-274
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• 2012

We in this paper discuss the strong law of large numbers for weighted sums of arrays of rowwise LNQD random variables by using a new exponential inequality of LNQD r.v.'s under suitable conditions and we obtain one of corollary.