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On Convergence Rates in the Marcinkiewicz–Zygmund Strong Law of Large Numbers

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Abstract

In 1967, Heyde and Rohatgi obtained two results on the rate of convergence in the Marcinkiewicz–Zygmund strong law of large numbers. In the present work, we show that the independence requirement in their theorems is unnecessary when the common law satisfies a suitable integrability condition.

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Acknowledgements

I would like to thank two anonymous referees for their insightful comments and for pointed out to me some errors and imprecisions in the original text of this paper. References [3, 13] was kindly suggested to me by an anonymous referee. This research is a contribution to the Project PRFU C00L03UN130120210002, funded by the DGRSDT-MESRS-Algeria.

Funding

This research was partially supported by the DGRSDT-MESRS-Algeria and the Laboratoire de Statistique et Modélisations Aléatoires.

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  1. Laboratoire de Statistique et Modélisations aléatoires Faculty of sciences, Abou Bekr Belkaid University, BP 119, 13000, Tlemcen, Algeria

    Fakhreddine Boukhari

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  1. Fakhreddine Boukhari
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Correspondence to Fakhreddine Boukhari.

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Boukhari, F. On Convergence Rates in the Marcinkiewicz–Zygmund Strong Law of Large Numbers. Results Math 76, 174 (2021). https://doi.org/10.1007/s00025-021-01487-2

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