On weak laws of large numbers for maximal partial sums of pairwise independent random variables
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 i...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-03-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.387/ |
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| author | Thành, Lê Vǎn |
| author_facet | Thành, Lê Vǎn |
| author_sort | Thành, Lê Vǎn |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fb29a6e06e994c0db8f1a35f45ef3b0b |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-fb29a6e06e994c0db8f1a35f45ef3b0b2025-02-07T11:07:00ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-03-01361G357758510.5802/crmath.38710.5802/crmath.387On weak laws of large numbers for maximal partial sums of pairwise independent random variablesThành, Lê Vǎn0Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, VietnamThis 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.387/ |
| spellingShingle | Thành, Lê Vǎn On weak laws of large numbers for maximal partial sums of pairwise independent random variables Comptes Rendus. Mathématique |
| title | On weak laws of large numbers for maximal partial sums of pairwise independent random variables |
| title_full | On weak laws of large numbers for maximal partial sums of pairwise independent random variables |
| title_fullStr | On weak laws of large numbers for maximal partial sums of pairwise independent random variables |
| title_full_unstemmed | On weak laws of large numbers for maximal partial sums of pairwise independent random variables |
| title_short | On weak laws of large numbers for maximal partial sums of pairwise independent random variables |
| title_sort | on weak laws of large numbers for maximal partial sums of pairwise independent random variables |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.387/ |
| work_keys_str_mv | AT thanhlevan onweaklawsoflargenumbersformaximalpartialsumsofpairwiseindependentrandomvariables |