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Limit theorems for dependent random variables with infinite means

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  • Bernou, Ismahen
  • Boukhari, Fakhreddine

Abstract

We investigate necessary and sufficient conditions for the convergence in probability of weighted averages of random variables with infinite means. The obtained results are valid for a wide range of dependence structures, they extend and improve the corresponding theorems of Adler (2012) and Nakata (2016), established in the independent case.

Suggested Citation

  • Bernou, Ismahen & Boukhari, Fakhreddine, 2022. "Limit theorems for dependent random variables with infinite means," Statistics & Probability Letters, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:stapro:v:189:y:2022:i:c:s0167715222001213
    DOI: 10.1016/j.spl.2022.109563
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    References listed on IDEAS

    as
    1. Nakata, Toshio, 2016. "Weak laws of large numbers for weighted independent random variables with infinite mean," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 124-129.
    2. Qi-Man Shao, 2000. "A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 13(2), pages 343-356, April.
    3. Sergey Utev & Magda Peligrad, 2003. "Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(1), pages 101-115, January.
    4. Fakhreddine Boukhari, 2021. "Weak laws of large numbers for maximal weighted sums of random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(1), pages 105-115, January.
    5. Wenzhi Yang & Lei Yang & Da Wei & Shuhe Hu, 2019. "The laws of large numbers for Pareto-type random variables with infinite means," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(12), pages 3044-3054, June.
    6. Rita Giuliano & Milto Hadjikyriakou, 2021. "On Exact Laws of Large Numbers for Oppenheim Expansions with Infinite Mean," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1579-1606, September.
    7. Boukhari, Fakhreddine, 2020. "The Marcinkiewics–Zygmund strong law of large numbers for dependent random variables," Statistics & Probability Letters, Elsevier, vol. 161(C).
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