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http://dx.doi.org/10.5831/HMJ.2012.34.2.241

ON ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF LNQD RANDOM VARIABLES  

Choi, Jeong-Yeol (School of mathematical Science and Institute of Basic Natural Science, Wonkwang University)
Kim, So-Youn (School of mathematical Science and Institute of Basic Natural Science, Wonkwang University)
Baek, Jong-Il (School of mathematical Science and Institute of Basic Natural Science, Wonkwang University)
Publication Information
Honam Mathematical Journal / v.34, no.2, 2012 , pp. 241-252 More about this Journal
Abstract
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.
Keywords
Strong law of large numbers; almost sure convergence; arrays; linearly negative quadrant random variables;
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Times Cited By KSCI : 2  (Citation Analysis)
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