English

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.

Keywords

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

R2 v1 2026-06-21T15:09:49.145Z