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On weak laws of large numbers for maximal partial sums of pairwise independent random variables
Authors: Lê Văn Thành
219    31
Comptes Rendus Mathématique
: 51     : 577-585
: https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.387/
: 1523_3_with_cover_on_weak_laws_of_large_numbers_for_maximal_partial_sums_of_pairwise_independent_random_variables.pdf
Publishing year: 5/2023
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.
Weak law of large numbers, Maximal partial sum; Pairwise independence
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