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CN 34-1054/N

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Complete convergence of weighted sums for extended ND random variables sequence under sub-linear expectation

  • College of Science,Guilin University of Technology, Guilin 541004, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2018.08.006
  • Received Date: 23 March 2018
  • Accepted Date: 17 April 2018
  • Rev Recd Date: 17 April 2018
  • Publish Date: 31 August 2018
    Abstract

  • Abstract

    The complete convergence of weighted sums for extended ND under sub-linear expectation was studied. With the condition of the p order Choquet integrals of the random variable being finite, the complete convergence of weighted sums for extended ND random variables sequence in the probability space was extended to the sub-linear expectations space.

    Abstract

    The complete convergence of weighted sums for extended ND under sub-linear expectation was studied. With the condition of the p order Choquet integrals of the random variable being finite, the complete convergence of weighted sums for extended ND random variables sequence in the probability space was extended to the sub-linear expectations space.
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    • References(12)
  • [1]
    PENG S. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation[J]. Stochastic Process, 2008, 118(12): 2223-2253.
    [2]
    PENG S. A new central limit theorem under sub-linear expectations[EB/OL]. [2018-03-01] https://arxiv.org/abs/0803.2656.
    [3]
    ZHANG L X. Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations[EB/OL]. [2018-03-01] https://arxiv.org/abs/ 1608.00710.
    [4]
    ZHANG L X. Exponential inequalities under sub-linear expectations with applications to laws of the iterated logarithm[J]. Science China, 2014, 59(12):2503-2526.
    [5]
    ZHANG L X. Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications[J]. Science China, 2016, 59(4):751-768.
    [6]
    WU Q, JIANG Y. Strong law of large numbers and Chover’s law of the iterated logarithm under sub-linear expectations[J]. Journal of Mathematical Analysis & Applications, 2018, 460(1): 252-270.
    [7]
    HU C, DATTA S, KOUL H L. A strong law of large numbers for sub-linear expectation under a general moment condition[J]. Statistics & Probability Letters, 2016, 119: 248-258.
    [8]
    WU Q. Complete convergence for negatively dependent sequences of random variables[J]. Journal of Inequalities & Applications, 2010, 2010(1):1-10.
    [9]
    WU Q. A complete convergence theorem for weighted sums of arrays of rowwise negatively dependent random variables[J]. Journal of Inequalities & Applications, 2012, 2012(1): 1-10.
    [10]
    孟兵, 吴群英. ND阵列加权乘积和的完全收敛性[J]. 纯粹数学与应用数学, 2010, 26(1):84-90.
    MENG Bing, WU Qunying. Complete convergence for weighted sums of arrays of ND random variables[J]. Pure and Applied Mathematics, 2010, 26(1):84-90.
    [11]
    甘师信, 陈平炎. NOD序列加权和的强收敛速度[J]. 数学物理学报, 2008, 28(2):283-290.
    GAN Shixin, CHEN Pingyan. Strong convergence rate of weighted sums for NOD sequences[J]. Acta Mathematica Scientia, 2008, 28(2):283-290.
    [12]
    ZHONG H, WU Q. Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables under sub-linear expectation[J]. Journal of Inequalities & Applications, 2017, 2017(1): 261.)
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    [1]
    PENG S. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation[J]. Stochastic Process, 2008, 118(12): 2223-2253.
    [2]
    PENG S. A new central limit theorem under sub-linear expectations[EB/OL]. [2018-03-01] https://arxiv.org/abs/0803.2656.
    [3]
    ZHANG L X. Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations[EB/OL]. [2018-03-01] https://arxiv.org/abs/ 1608.00710.
    [4]
    ZHANG L X. Exponential inequalities under sub-linear expectations with applications to laws of the iterated logarithm[J]. Science China, 2014, 59(12):2503-2526.
    [5]
    ZHANG L X. Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications[J]. Science China, 2016, 59(4):751-768.
    [6]
    WU Q, JIANG Y. Strong law of large numbers and Chover’s law of the iterated logarithm under sub-linear expectations[J]. Journal of Mathematical Analysis & Applications, 2018, 460(1): 252-270.
    [7]
    HU C, DATTA S, KOUL H L. A strong law of large numbers for sub-linear expectation under a general moment condition[J]. Statistics & Probability Letters, 2016, 119: 248-258.
    [8]
    WU Q. Complete convergence for negatively dependent sequences of random variables[J]. Journal of Inequalities & Applications, 2010, 2010(1):1-10.
    [9]
    WU Q. A complete convergence theorem for weighted sums of arrays of rowwise negatively dependent random variables[J]. Journal of Inequalities & Applications, 2012, 2012(1): 1-10.
    [10]
    孟兵, 吴群英. ND阵列加权乘积和的完全收敛性[J]. 纯粹数学与应用数学, 2010, 26(1):84-90.
    MENG Bing, WU Qunying. Complete convergence for weighted sums of arrays of ND random variables[J]. Pure and Applied Mathematics, 2010, 26(1):84-90.
    [11]
    甘师信, 陈平炎. NOD序列加权和的强收敛速度[J]. 数学物理学报, 2008, 28(2):283-290.
    GAN Shixin, CHEN Pingyan. Strong convergence rate of weighted sums for NOD sequences[J]. Acta Mathematica Scientia, 2008, 28(2):283-290.
    [12]
    ZHONG H, WU Q. Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables under sub-linear expectation[J]. Journal of Inequalities & Applications, 2017, 2017(1): 261.)
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