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Marcinkiewicz type complete convergence for weighted sums under sub-linear expectations

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

Funds:  Supported by National Science Foundation of China (11661029), Program of the Guangxi China Science Foundation (2015GXNSFAA139008)
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2018.02.001
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  • Author Bio:

    YU Donglin, male, born in 1993, master. Research field: Probability limit theory. E-mail: daliyu1st@163.com

  • Corresponding author: WU Qunying
  • Received Date: 15 December 2017
  • Rev Recd Date: 19 January 2018
  • Publish Date: 28 February 2018
    Abstract

  • Abstract

    The complete convergence theorems under sub-linear expectations was studied. As applications, Marcinkiewicz type complete convergence for weighted sums of END random

    Abstract

    The complete convergence theorems under sub-linear expectations was studied. As applications, Marcinkiewicz type complete convergence for weighted sums of END random
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    • References(16)
  • [1]
    PENG S. G-expectation, g-brownian motion and related stochastic calculus of ito type[J]. Stochastic Analysis & Applications, 2006, 2(4),541-567.
    [2]
    PENG S. Multi-dimensional g-brownian motion and related stochastic calculus under g-expectation[J]. Stochastic Processes & Their Applications, 2008, 118(12): 2223-2253.
    [3]
    PENG S. A new central limit theorem under sublinear expectations[J]. Mathematics, 2008, 53(8): 1989-1994.
    [4]
    ZHANG L X. Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations[DB/OL]. arXiv.ORG: 1608.00710, 2016.
    [5]
    ZHANG L X. Rosenthals inequalities for independent and negatively dependent random variables under sub-linear expectations with applications[J]. Science China Mathematics, 2016, 59(4): 751-768.
    [6]
    ZHANG L X. Self-normalized moderate deviation and laws of the iterated logarithm under G-Expectation[J]. Communications in Mathematics and Statistics, 2016, 4(2): 229-263.
    [7]
    ZHANG L X. Exponential inequalities under the sub-linear expectations with applications to laws of the iterated[J]. Science China Mathematics, 2016, 59(12): 2503-2526.
    [8]
    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 and Applications, 2018,460(1):252-270.
    [9]
    HSU P L, ROBBINS H. Complete convergence and the law of large numbers[J]. Proceedings of the National Academy of Sciences of the United States of America, 1947, 33(2): 25-31.
    [10]
    SUNG S H. On the strong convergence for weighted sums of random variables[J]. Statistical Papers, 2011, 52(2): 447-454.
    [11]
    CAI G H. Strong laws for weighted sums of NA random variables[J]. Metrika, 2008, 68(3): 323-331.
    [12]
    WU Q, JIANG Y. Complete convergence and complete moment convergence for negatively associated sequences of random variables[J]. Journal of Inequalities & Applications, 2016, 2016:157.
    [13]
    HUANG H, PENG J, WU X, et al. Complete convergence and complete moment convergence for arrays of rowwise ANA random variables[J]. Journal of Inequalities & Applications,2016, 2016:72.
    [14]
    SHEN A, XUE M, WANG W. Complete convergence for weighted sums of extended negatively dependent random variables[J]. Communications in Statistics: Theory and Methods,2017, 46(3): 1433-1444.
    [15]
    HUANG H, WANG D. A note on the strong limit theorem for weighted sums of sequences of negatively dependent random variables[J]. Journal of Inequalities & Applications, 2012, 2012:233.
    [16]
    DENIS L, HU M, PENG S. Function spaces and capacity related to a sublinear expectation: Application to g-brownian motion paths[J].Potential Analysis,2011, 34(2): 139-161.
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    [1]
    PENG S. G-expectation, g-brownian motion and related stochastic calculus of ito type[J]. Stochastic Analysis & Applications, 2006, 2(4),541-567.
    [2]
    PENG S. Multi-dimensional g-brownian motion and related stochastic calculus under g-expectation[J]. Stochastic Processes & Their Applications, 2008, 118(12): 2223-2253.
    [3]
    PENG S. A new central limit theorem under sublinear expectations[J]. Mathematics, 2008, 53(8): 1989-1994.
    [4]
    ZHANG L X. Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations[DB/OL]. arXiv.ORG: 1608.00710, 2016.
    [5]
    ZHANG L X. Rosenthals inequalities for independent and negatively dependent random variables under sub-linear expectations with applications[J]. Science China Mathematics, 2016, 59(4): 751-768.
    [6]
    ZHANG L X. Self-normalized moderate deviation and laws of the iterated logarithm under G-Expectation[J]. Communications in Mathematics and Statistics, 2016, 4(2): 229-263.
    [7]
    ZHANG L X. Exponential inequalities under the sub-linear expectations with applications to laws of the iterated[J]. Science China Mathematics, 2016, 59(12): 2503-2526.
    [8]
    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 and Applications, 2018,460(1):252-270.
    [9]
    HSU P L, ROBBINS H. Complete convergence and the law of large numbers[J]. Proceedings of the National Academy of Sciences of the United States of America, 1947, 33(2): 25-31.
    [10]
    SUNG S H. On the strong convergence for weighted sums of random variables[J]. Statistical Papers, 2011, 52(2): 447-454.
    [11]
    CAI G H. Strong laws for weighted sums of NA random variables[J]. Metrika, 2008, 68(3): 323-331.
    [12]
    WU Q, JIANG Y. Complete convergence and complete moment convergence for negatively associated sequences of random variables[J]. Journal of Inequalities & Applications, 2016, 2016:157.
    [13]
    HUANG H, PENG J, WU X, et al. Complete convergence and complete moment convergence for arrays of rowwise ANA random variables[J]. Journal of Inequalities & Applications,2016, 2016:72.
    [14]
    SHEN A, XUE M, WANG W. Complete convergence for weighted sums of extended negatively dependent random variables[J]. Communications in Statistics: Theory and Methods,2017, 46(3): 1433-1444.
    [15]
    HUANG H, WANG D. A note on the strong limit theorem for weighted sums of sequences of negatively dependent random variables[J]. Journal of Inequalities & Applications, 2012, 2012:233.
    [16]
    DENIS L, HU M, PENG S. Function spaces and capacity related to a sublinear expectation: Application to g-brownian motion paths[J].Potential Analysis,2011, 34(2): 139-161.
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