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.
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Lê Vǎn Thành 1
@article{CRMATH_2023__361_G3_577_0, author = {L\^e Vǎn Th\`anh}, title = {On weak laws of large numbers for maximal partial sums of pairwise independent random variables}, journal = {Comptes Rendus. Math\'ematique}, pages = {577--585}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.387}, language = {en}, }
TY - JOUR AU - Lê Vǎn Thành TI - On weak laws of large numbers for maximal partial sums of pairwise independent random variables JO - Comptes Rendus. Mathématique PY - 2023 SP - 577 EP - 585 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.387 LA - en ID - CRMATH_2023__361_G3_577_0 ER -
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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