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On Exact Laws of Large Numbers for Oppenheim Expansions with Infinite Mean

Author

Listed:
  • Rita Giuliano

    (Università di Pisa)

  • Milto Hadjikyriakou

    (University of Central Lancashire)

Abstract

In this work, we investigate the asymptotic behaviour of weighted partial sums of a particular class of random variables related to Oppenheim series expansions. More precisely, we verify convergence in probability as well as almost sure convergence to a strictly positive and finite constant without assuming any dependence structure or the existence of means. Results of this kind are known as exact weak and exact strong laws.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:3:d:10.1007_s10959-020-01010-3
    DOI: 10.1007/s10959-020-01010-3
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    References listed on IDEAS

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    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. André Adler, 2007. "Laws of Large Numbers for Asymmetrical Cauchy Random Variables," International Journal of Stochastic Analysis, Hindawi, vol. 2007, pages 1-6, January.
    3. 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.
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    Cited by:

    1. Bernou, Ismahen & Boukhari, Fakhreddine, 2022. "Limit theorems for dependent random variables with infinite means," Statistics & Probability Letters, Elsevier, vol. 189(C).

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