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

DOI10.5802/CRMATH.387arXiv2208.00130MaRDI QIDQ6406518

Publication date: 29 July 2022

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.

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

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