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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)
  • Received : 2012.03.29
  • Accepted : 2012.04.23
  • Published : 2012.06.25

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.

Acknowledgement

Supported by : Wonkwang University

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