2 citations · 4 across the 7 of their papers we have counts for
7 papers
Non-uniform bounds for non-normal approximation via Stein's method with applications to the Curie--Weiss model and the imitative monomer-dimer model
Lê Vǎn Thành, Nguyen Ngoc Tu
This paper establishes a non-uniform Berry--Esseen bound for non-normal approximation using Stein's method. The main theorem generalizes the result of the authors in [Comptes Rendu…
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…
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…
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…
On the -type Strong Law of Large Numbers for Sequences of Independent Random Variables
Lê Vǎn Thành
Li, Qi, and Rosalsky (Trans. Amer. Math. Soc., 2016) introduced a refinement of the Marcinkiewicz--Zygmund strong law of large numbers (SLLN), so-called the -type SLLN, wher…
Optimal Bounds in Normal Approximation for Many Interacting Worlds
Louis H. Y. Chen, Lê Vǎn Thành
In this paper, we use Stein's method to obtain optimal bounds, both in Kolmogorov and in Wasserstein distance, in the normal approximation for the empirical distribution of the gro…
Error bounds in normal approximation for the squared-length of total spin in the mean field classical -vector models
Lê Vǎn Thành, Nguyen Ngoc Tu
This paper gives the Kolmogorov and Wasserstein bounds in normal approximation for the squared-length of total spin in the mean field classical -vector models. The Kolmogorov bo…