2023
DOI: 10.5802/crmath.387
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On weak laws of large numbers for maximal partial sums of pairwise independent random variables

Abstract: 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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