Stein's method and normal approximation of Poisson functionals

Giovanni Peccati; Josep Lluís Solé; Murad S. Taqqu; Frederic Utzet

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arXiv · 0807.5035

Stein's method and normal approximation of Poisson functionals

Giovanni Peccati·Josep Lluís Solé·Murad S. Taqqu·Frederic Utzet

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Abstract

We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Esséen bounds in Central Limit Theorems (CLTs) involving multiple Wiener-Itô integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck Lévy processes.

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BibTeX RIS

Giovanni Peccati, Josep Lluís Solé, Murad S. Taqqu, Frederic Utzet. 2008-07-31. Stein's method and normal approximation of Poisson functionals. https://arxiv.org/abs/0807.5035

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