This paper is devoted to the rate of convergence problem in the central limit theorem for sums of independent identically distributed random variables with regular probability density function. The method we use depends strictly on Fourier based metrics, and yields Berry-Esseen like bounds for the convergence towards both a normal and a stable law in various Sobolev norms.
Publié le : 2002-07-04
Classification:
Fourier-based distances,
Central-Limit Theorem,
Berry Esseen estimates,
MSC: 60F05,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-01312340,
author = {Goudon, Thierry and Junca, St\'ephane and Toscani, Giuseppe},
title = {Fourier-based distances and Berry-Esseen like inequalities},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01312340}
}
Goudon, Thierry; Junca, Stéphane; Toscani, Giuseppe. Fourier-based distances and Berry-Esseen like inequalities. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-01312340/