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math.PR2024
On Rio's proof of limit theorems for dependent random fields
Lê Vǎn Thành
This paper presents an exposition of Rio's proof of the strong law of large numbers and extends his method to random fields. In addition to considering the rate of convergence in t…
math.PR2022
On weak laws of large numbers for maximal partial sums of pairwise independent random variables
Lê Vǎn Thành
This paper develops Rio's method [C. R. Acad. Sci. Paris Sér. I Math., 1995] to prove the weak law of large numbers for maximal partial sums of pairwise independent random variable…
math.PR2022★ 1 cited
On a new concept of stochastic domination and the laws of large numbers
Lê Vǎn Thành
Consider a sequence of positive integers , and an array of nonnegative real numbers satisfying $\sup_{n\ge 1}\sum_{i=1}^{k_n}a_{n,i…