• Title, Summary, Keyword: Complete convergence

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EQUIVALENT CONDITIONS OF COMPLETE MOMENT CONVERGENCE AND COMPLETE INTEGRAL CONVERGENCE FOR NOD SEQUENCES

  • Deng, Xin;Wang, Xuejun
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.917-933
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    • 2017
  • In this paper, seven equivalent conditions of complete moment convergence and complete integral convergence for negatively orthant dependent (NOD, in short) sequences are shown under two cases: identical distribution and stochastic domination. The results obtained in the paper improve and generalize the corresponding ones of Liang et al. [10]). In addition, an extension of the Baum-Katz complete convergence theorem: six equivalent conditions of complete convergence is established.

ON COMPLETE CONVERGENCE AND COMPLETE MOMENT CONVERGENCE FOR A CLASS OF RANDOM VARIABLES

  • Wang, Xuejun;Wu, Yi
    • Journal of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.877-896
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    • 2017
  • In this paper, the complete convergence and complete moment convergence for a class of random variables satisfying the Rosenthal type inequality are investigated. The sufficient and necessary conditions for the complete convergence and complete moment convergence are provided. As applications, the Baum-Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for a class of random variables satisfying the Rosenthal type inequality are established. The results obtained in the paper extend the corresponding ones for some dependent random variables.

COMPLETE CONVERGENCE AND COMPLETE MOMENT CONVERGENCE THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF ROWWISE EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES

  • Huang, Haiwu;Zhang, Qingxia
    • 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.

THE COMPLETE MOMENT CONVERGENCE FOR ARRAY OF ROWWISE ENOD RANDOM VARIABLES

  • Ryu, Dae-Hee
    • Honam Mathematical Journal
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    • v.33 no.3
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    • pp.393-405
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    • 2011
  • In this paper we obtain the complete moment convergence for an array of rowwise extended negative orthant dependent random variables. By using the result we can prove the complete moment convergence for some positively orthant dependent sequence satisfying the extended negative orthant dependence.

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.

ON THE CONVERGENCE FOR ND RANDOM VARIABLES WITH APPLICATIONS

  • Baek, Jong-Il;Seo, Hye-Young
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1351-1361
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    • 2011
  • We in this paper study the complete convergence and almost surely convergence for arrays of rowwise pairwise negatively dependent(ND) random variables (r.${\upsilon}$.'s) which are dominated randomly by some random variables and obtain a result dealing with complete convergence of linear processes.

A COMPLETE CONVERGENCE FOR LINEAR PROCESS UNDER ρ-MIXING ASSUMPTION

  • Kim, Hyun-Chull;Ryu, Dae-Hee
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.1
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    • pp.127-136
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    • 2010
  • For the maximum partial sum of linear process generated by a doubly infinite sequence of identically distributed $\rho$-mixing random variables with mean zeros, a complete convergence is obtained under suitable conditions.

Complete convergence for weighted sums of AANA random variables

  • Kim, Tae-Sung;Ko, Mi-Hwa
    • Proceedings of the Korean Statistical Society Conference
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    • pp.209-213
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    • 2002
  • We study maximal second moment inequality and derive complete convergence for weighted sums of asymptotically almost negatively associated(AANA) random variables by applying this inequality. 2000 Mathematics Subject Classification : 60F05

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