On weak laws of large numbers for maximal partial sums of pairwise independent random variables
Probability
2022-08-02 v1
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.
Keywords
Cite
@article{arxiv.2208.00130,
title = {On weak laws of large numbers for maximal partial sums of pairwise independent random variables},
author = {Lê Vǎn Thành},
journal= {arXiv preprint arXiv:2208.00130},
year = {2022}
}
Comments
10 pages, To appear in Comptes Rendus Mathematique