Zobrazeno 1 - 10
of 87
pro vyhledávání: '"Chen, Louis H. Y."'
We present an assessment of the distance in total variation of \textit{arbitrary} collection of prime factor multiplicities of a random number in $[n]=\{1,\dots, n\}$ and a collection of independent geometric random variables. More precisely, we impo
Externí odkaz:
http://arxiv.org/abs/2111.07361
Autor:
Chen, Louis H. Y.
This paper is a short exposition of Stein's method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of Stein identities. Through examples, it provides glim
Externí odkaz:
http://arxiv.org/abs/2104.08302
We present a new perspective of assessing the rates of convergence to the Gaussian and Poisson distributions in the Erd\"os-Kac theorem for additive arithmetic functions $\psi$ of a random integer $J_n$ uniformly distributed over $\{1,...,n\}$. Our a
Externí odkaz:
http://arxiv.org/abs/2102.05094
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
We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of normal approxim
Externí odkaz:
http://arxiv.org/abs/2004.05026
Applying an inductive technique for Stein and zero bias couplings yields Berry-Esseen theorems for normal approximation for two new examples. The conditions of the main results do not require that the couplings be bounded. Our two applications, one t
Externí odkaz:
http://arxiv.org/abs/1903.09319
In this paper, we obtain uniform and non-uniform bounds on the Kolmogorov distance in the normal approximation for Jack deformations of the character ratio, by using Stein's method and zero-bias couplings. Our uniform bound comes very close to that c
Externí odkaz:
http://arxiv.org/abs/1902.03476
In this paper we establish a framework for normal approximation for white noise functionals by Stein's method and Hida calculus. Our work is inspired by that of Nourdin and Peccati (Probab. Theory Relat. Fields 145, 75-118, 2009), who combined Stein'
Externí odkaz:
http://arxiv.org/abs/1701.00360
Autor:
Barbour, Andrew D., Chen, Louis H. Y.
The paper presents a general introduction to the astonishing method for deriving probability approximations that was invented by Charles Stein around 50 years ago.
Externí odkaz:
http://arxiv.org/abs/1411.1179
Autor:
Chen, Louis H. Y.
Stein's method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation the functional equation is a first order differential equation. Malliavin calculus is an infinite-dimensional diff
Externí odkaz:
http://arxiv.org/abs/1407.5172