• Title, Summary, Keyword: almost sure convergence

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Almost sure convergence for weighted sums of I.I.D. random variables (II)

  • Sung, Soo-Hak
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.419-425
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    • 1996
  • Let ${X, X_n, n \geq 1}$ be a sequence of independent and identically distributed(i.i.d) random variables with EX = 0 and $E$\mid$X$\mid$^p < \infty$ for some $p \geq 1$. Let ${a_{ni}, 1 \leq i \leq n, n \geq 1}$ be a triangular arrary of constants. The almost sure(a.s) convergence of weighted sums $\sum_{i=1}^{n} a_{ni}X_i$ can be founded in Choi and Sung[1], Chow[2], Chow and Lai[3], Li et al. [4], Stout[6], Sung[8], Teicher[9], and Thrum[10].

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ON THE ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF 2-DIMENSIONAL ARRAYS OF POSITIVE DEPENDENT RANDOM VARIABLES

  • Kim, Tae-Sung;Baek, Ho-Yu;Han, Kwang-Hee
    • Communications of the Korean Mathematical Society
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    • v.14 no.4
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    • pp.797-804
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    • 1999
  • In this paper we derive the almost sure convergence of weighted sums of 2-dimensional arrays of random variables which are either pairwise positive quadrant dependent or associated. Our re-sults imply and extension of Etemadi's(1983) strong laws of large numbers for weighted sums of nonnegative random variables to the 2-dimensional case.

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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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Almost Sure Convergence for Asymptotically Almost Negatively Associated Random Variable Sequences

  • Baek, Jong-Il
    • Communications for Statistical Applications and Methods
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    • v.16 no.6
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    • pp.1013-1022
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    • 2009
  • We in this paper study the almost sure convergence for asymptotically almost negatively associated(AANA) random variable sequences and obtain some new results which extend and improve the result of Jamison et al. (1965) and Marcinkiewicz-Zygumnd strong law types in the form given by Baum and Katz (1965), three-series theorem.

THE ALMOST SURE CONVERGENCE OF WEIGHTED AVERAGES UNDER NEGATIVE QUADRANT DEPENDENCE

  • Ryu, Dae-Hee
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.885-893
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    • 2009
  • In this paper we study the strong law of large numbers for weighted average of pairwise negatively quadrant dependent random variables. This result extends that of Jamison et al.(Convergence of weight averages of independent random variables Z. Wahrsch. Verw Gebiete(1965) 4 40-44) to the negative quadrant dependence.

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THE ALMOST SURE CONVERGENCE FOR THE IDENTICALLY DISTRIBUTED NEGATIVELY ASSOCIATED RANDOM VARIABLES WITH INFINITE MEANS

  • Kim, Hyun-Chull
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.363-372
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    • 2010
  • In this paper we prove the almost sure convergence of partial sums of identically distributed and negatively associated random variables with infinite expectations. Some results in Kruglov[Kruglov, V., 2008 Statist. Probab. Lett. 78(7) 890-895] are considered in the case of negatively associated random variables.

ON ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF LNQD RANDOM VARIABLES

  • Choi, Jeong-Yeol;Kim, So-Youn;Baek, Jong-Il
    • Honam Mathematical Journal
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    • v.34 no.2
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    • pp.241-252
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    • 2012
  • 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.