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 Electronic Journal of Probability > Vol. 15(2010) > Paper 48 open journal systems 


Multi-dimensional Gaussian fluctuations on the Poisson space

Peccati Giovanni, Université du Luxembourg
Cengbo Zheng, Université Paris Ouest, Nanterre la Défense


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, Solé, Taqqu and Utzet. Several explicit examples (including in particular vectors of linear and non-linear functionals of Ornstein-Uhlenbeck Lévy processes) are discussed in detail.


Full text: PDF

Pages: 1487-1527

Published on: October 15, 2010
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Electronic Journal of Probability. ISSN: 1083-6489