• Title, Summary, Keyword: sums of independent random variables

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AN EXTENSION OF RANDOM SUMMATIONS OF INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES

  • Giang, Le Truong;Hung, Tran Loc
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.605-618
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    • 2018
  • The main goal of this paper is to study an extension of random summations of independent and identically distributed random variables when the number of summands in random summation is a partial sum of n independent, identically distributed, non-negative integer-valued random variables. Some characterizations of random summations are considered. The central limit theorems and weak law of large numbers for extended random summations are established. Some weak limit theorems related to geometric random sums, binomial random sums and negative-binomial random sums are also investigated as asymptotic behaviors of extended random summations.

THE STRONG LAWS OF LARGE NUMBERS FOR WEIGHTED SUMS OF PAIRWISE QUADRANT DEPENDENT RANDOM VARIABLES

  • Kim, Tae-Sung;Baek, Jong-Il
    • 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.

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SLIN FOR WEIGHTED SUMS OF STOCHASTICALLY DOMINATED PAIRWISE INDEPENDENT RANDOM VARIABLES

  • Sung, Soo-Hak
    • Communications of the Korean Mathematical Society
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    • v.13 no.2
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    • pp.377-384
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    • 1998
  • Let ${X_n,n \geq 1}$ be a sequence of stochatically dominated pairwise independent random variables. Let ${a_n, n \geq 1}$ and ${b_n, n \geq 1}$ be seqence of constants such that $a_n \neq 0$ and $0 < b_n \uparrow \infty$. A strong law large numbers of the form $\sum^{n}_{j=1}{a_j X_i//b_n \to 0$ almost surely is obtained.

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ON THE COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES

  • SEO, HYE-YOUNG;SHII, DA-LI;BAEK, JONG-IL
    • Journal of applied mathematics & informatics
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    • v.37 no.3_4
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    • pp.207-217
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    • 2019
  • We are presented of several basic properties for negatively superadditive dependent(NSD) random variables. By using this concept we are obtained complete convergence for maximum partial sums of rowwise NSD random variables. These results obtained in this paper generalize a corresponding ones for independent random variables and negatively associated random variables.

ON THE STRONG LAW OF LARGE NUMBERS FOR WEIGHTED SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES

  • SHEN, AITING
    • Journal of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.45-55
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    • 2016
  • Let {$X_n,n{\geq}1$} be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums ${\frac{1}{g(n)}}{\sum_{i=1}^{n}}{\frac{X_i}{h(i)}}$ of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law of large numbers and Marcinkiewicz-Zygmund strong law of large numbers for negatively superadditive dependent random variables are obtained. Our results generalize the corresponding ones for independent random variables and negatively associated random variables.

ON THE COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES

  • Qiu, Dehua;Chen, Pingyan;Antonini, Rita Giuliano;Volodin, Andrei
    • 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.