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On the strong convergence of weighted sums of widely dependent random variables

Author

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  • Dongya Cheng
  • Wenhai Zhang
  • Yuebao Wang

Abstract

For widely dependent random variables, we present some results on the strong convergence of weighted sums, including results on almost surely (a.s.) and complete convergence. To this end, we verified some Borel–Cantelli lemmas of the widely dependent random variables. The above-mentioned random variables contain common negatively dependent random variables, some positively dependent random variables, and some others; therefore, the obtained results extend and improve some existing results.

Suggested Citation

  • Dongya Cheng & Wenhai Zhang & Yuebao Wang, 2016. "On the strong convergence of weighted sums of widely dependent random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(21), pages 6447-6460, November.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:21:p:6447-6460
    DOI: 10.1080/03610926.2014.922988
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    Cited by:

    1. Jinyu Zhou & Jigao Yan & Dongya Cheng, 2024. "Strong consistency of tail value-at-risk estimator and corresponding general results under widely orthant dependent samples," Statistical Papers, Springer, vol. 65(6), pages 3357-3394, August.

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