Stein’s method and Normal approximation of Poisson functionals
Files
First author draft
Date
2010-03-01
Authors
Peccati, G.
Sole, J. L.
Taqqu, Murad S.
Utzet, F.
Version
First author draft
OA Version
Citation
G. Peccati, J.L. Sole, M.S. Taqqu, F. Utzet. 2010. "STEIN'S METHOD AND NORMAL APPROXIMATION OF POISSON FUNCTIONALS." ANNALS OF PROBABILITY, Volume 38, Issue 2, pp. 443 - 478 (36). https://doi.org/10.1214/09-AOP477
Abstract
We combine Stein’s method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry–Esséen bounds in Central limit theorems (CLTs) involving multiple Wiener–Itô integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein–Uhlenbeck Lévy processes.