On weak laws of large numbers for maximal partial sums of pairwise independent random variables
Abstract
This paper develops Rio's method [C. R. Acad. Sci. Paris S\'er. 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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