On weak laws of large numbers for maximal partial sums of pairwise independent random variables
Tác giả: Lê Văn Thành
Comptes Rendus Mathématique
Quyển: 51 Trang: 577-585
Năm xuất bản: 5/2023
Tóm tắt
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.
Từ khóa
Weak law of large numbers, Maximal partial sum; Pairwise independence
