Multi-dimensional Gaussian fluctuations on the Poisson space

Details Multi-dimensional Gaussian fluctuations on the Poisson space Multi-dimensional Gaussian fluctuations on the Poisson space

2010-04-13

arxiv.org/abs/1004.2175v1

Mathematics

Probability

40 pages

Scientific paper

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.

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