Comptes Rendus
Probabilités
On weak laws of large numbers for maximal partial sums of pairwise independent random variables
Lê Vǎn Thành1
1 Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, Vietnam
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 577-585.

This paper develops Rio’s method [11] to prove the weak law of large numbers for maximal partial sums of pairwise independent random variables. The method allows us to avoid using the Kolmogorov maximal inequality. As an application, a weak law of large numbers for maximal partial sums of pairwise independent random variables under a uniform integrability condition is also established. The sharpness of the result is illustrated by an example.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.387
Classification : 60F05
Lê Vǎn Thành 1

1 Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, Vietnam
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Lê Vǎn Thành. On weak laws of large numbers for maximal partial sums of pairwise independent random variables. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 577-585. doi : 10.5802/crmath.387. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.387/

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