Stein's method on Wiener chaos
| dc.creator | Nourdin, Ivan | |
| dc.creator | Peccati, Giovanni | |
| dc.date | 2007-12-18 | |
| dc.date | 2008-05-10 | |
| dc.date.accessioned | 2026-07-07T09:37:49Z | |
| dc.date.available | 2026-07-07T09:37:49Z | |
| dc.description | We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. We also prove results concerning random variables admitting a possibly infinite Wiener chaotic decomposition. Our approach generalizes, refines and unifies the central and non-central limit theorems for multiple Wiener-Itô integrals recently proved (in several papers, from 2005 to 2007) by Nourdin, Nualart, Ortiz-Latorre, Peccati and Tudor. We apply our techniques to prove Berry-Esséen bounds in the Breuer-Major CLT for subordinated functionals of fractional Brownian motion. By using the well-known Mehler's formula for Ornstein-Uhlenbeck semigroups, we also recover a technical result recently proved by Chatterjee, concerning the Gaussian approximation of functionals of finite-dimensional Gaussian vectors. | |
| dc.description | 39 pages; Two sections added; To appear in PTRF | |
| dc.identifier | https://arxiv.org/abs/0712.2940 | |
| dc.identifier | http://arxiv.org/abs/0712.2940 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160591 | |
| dc.subject | Probability | |
| dc.subject | 60F05; 60G15; 60H05; 60H07 | |
| dc.title | Stein's method on Wiener chaos | |
| dc.type | text |