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arXiv · 2208.00130

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

Lê Vǎn Thành
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Abstract

This paper develops Rio's method [C. R. Acad. Sci. Paris S\'{e}r. I Math., 1995] 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. 2022-07-30. On weak laws of large numbers for maximal partial sums of pairwise independent random variables. https://arxiv.org/abs/2208.00130

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