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On the strong convergence properties for weighted sums of negatively orthant dependent random variables

  • Xin Deng
  • Xu-fei Tang
  • Shi-jie Wang
  • Xue-jun Wang
Article

Abstract

In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent (NOD) random variables are investigated. Let {X n , n ≥ 1} be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.

Keywords

strong convergence negatively orthant dependent random variables stochastic domination 

MR Subject Classification

60F15 

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Notes

Acknowledgements

The authors are most grateful to the anonymous referee for careful reading of the manuscript and valuable suggestions which helped in improving an earlier version of this paper.

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Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Xin Deng
    • 1
  • Xu-fei Tang
    • 1
  • Shi-jie Wang
    • 1
  • Xue-jun Wang
    • 1
  1. 1.School of Mathematical SciencesAnhui UniversityHefeiChina

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