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Weak laws of large numbers for maximal weighted sums of random variables

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  • Fakhreddine Boukhari

Abstract

In this paper, we establish a weak law of large numbers for a class of weighted sums of random variables introduced by Jajte (2003). The obtained method allows us to deduce a generalized version of the Marcinkiewicz-Zygmund weak law of large numbers and to strengthen several known results, such as those of Gut (2004) and Naderi et al. (2018). Finally, an application to randomly indexed sums is presented.

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  • 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.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:1:p:105-115
    DOI: 10.1080/03610926.2019.1630437
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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).
    2. Fakhreddine Boukhari, 2022. "On a Weak Law of Large Numbers with Regularly Varying Normalizing Sequences," Journal of Theoretical Probability, Springer, vol. 35(3), pages 2068-2079, September.

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