Zobrazeno 1 - 10
of 50
pro vyhledávání: '"Thành, Lê Vǎn"'
Autor:
Thành, Lê Vǎn
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G3, Pp 577-585 (2023)
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
Externí odkaz:
https://doaj.org/article/fb29a6e06e994c0db8f1a35f45ef3b0b
Autor:
Thành, Lê Vǎn
Publikováno v:
Comptes Rendus. Mathématique, Vol 358, Iss 11-12, Pp 1231-1238 (2021)
This paper proves the Baum–Katz theorem for sequences of pairwise independent identically distributed random variables with general norming constants under optimal moment conditions. The proof exploits some properties of slowly varying functions an
Externí odkaz:
https://doaj.org/article/cdcb5deba49f486cb28d99a291cb1e11
Autor:
Thành, Lê Vǎn
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 ineq
Externí odkaz:
http://arxiv.org/abs/2208.00130
Autor:
Thành, Lê Vǎn
Consider a sequence of positive integers $\{k_n,n\ge1\}$, and an array of nonnegative real numbers $\{a_{n,i},1\le i\le k_n,n\ge1\}$ satisfying $\sup_{n\ge 1}\sum_{i=1}^{k_n}a_{n,i}=C_0\in (0,\infty).$ This paper introduces the concept of $\{a_{n,i}\
Externí odkaz:
http://arxiv.org/abs/2207.06715
Autor:
Dzung, Nguyen Chi, Thành, Lê Vǎn
This note develops Rio's proof [C. R. Math. Acad. Sci. Paris, 1995] of the rate of convergence in the Marcinkiewicz--Zygmund strong law of large numbers to the case of sums of dependent random variables with regularly varying normalizing constants. I
Externí odkaz:
http://arxiv.org/abs/2107.12690
This paper establishes complete convergence for weighted sums and the Marcinkiewicz--Zygmund-type strong law of large numbers for sequences of negatively associated and identically distributed random variables $\{X,X_n,n\ge1\}$ with general normalizi
Externí odkaz:
http://arxiv.org/abs/2103.00114
Autor:
Thành, Lê Vǎn
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 $(p,q)$-type SLLN, where $00$. They obtained sets of necessary and sufficient co
Externí odkaz:
http://arxiv.org/abs/2008.01306
Autor:
Chen, Louis H. Y., Thành, Lê Vǎn
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 ground state of a many-interacting-worlds harmonic oscillator proposed by
Externí odkaz:
http://arxiv.org/abs/2006.11027
Autor:
Thành, Lê Vǎn, Tu, Nguyen Ngoc
Publikováno v:
Electronic Communications in Probability, 24 (2019), no. 16, 1--12
This paper gives the Kolmogorov and Wasserstein bounds in normal approximation for the squared-length of total spin in the mean field classical $N$-vector models. The Kolmogorov bound is new while the Wasserstein bound improves a result obtained rece
Externí odkaz:
http://arxiv.org/abs/1903.02216