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arXiv · 1004.2175

Multi-dimensional Gaussian fluctuations on the Poisson space

Giovanni Peccati·Cengbo Zheng
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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.

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Giovanni Peccati, Cengbo Zheng. 2010-04-13. Multi-dimensional Gaussian fluctuations on the Poisson space. https://arxiv.org/abs/1004.2175

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