Multi-dimensional Gaussian fluctuations on the Poisson space
Probability
2010-04-14 v1
Abstract
We study multi-dimensional normal approximations on the Poisson space by means of Malliavin calculus, Stein's method and probabilistic interpolations. Our results yield new multi-dimensional central limit theorems for multiple integrals with respect to Poisson measures -- thus significantly extending previous works by Peccati, Sol\'e, Taqqu and Utzet. Several explicit examples (including in particular vectors of linear and non-linear functionals of Ornstein-Uhlenbeck L\'evy processes) are discussed in detail.
Cite
@article{arxiv.1004.2175,
title = {Multi-dimensional Gaussian fluctuations on the Poisson space},
author = {Giovanni Peccati and Cengbo Zheng},
journal= {arXiv preprint arXiv:1004.2175},
year = {2010}
}
Comments
40 pages