On weak laws of large numbers for maximal partial sums of pairwise independent random variables

Lê Vǎn Thành

doi:10.5802/crmath.387

Probabilités

On weak laws of large numbers for maximal partial sums of pairwise independent random variables

Lê Vǎn Thành ¹

¹ Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, Vietnam

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 577-585.

Résumé

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 : 2022-02-12
Accepté le : 2022-05-30
Publié le : 2023-03-02

DOI : 10.5802/crmath.387

Classification : 60F05

Affiliations des auteurs :

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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     title = {On weak laws of large numbers for maximal partial sums of pairwise independent random variables},
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     pages = {577--585},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.387},
     language = {en},
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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/

Bibliographie
Cité par

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