Stein’s method and Normal approximation of Poisson functionals
Sole, J. L.
Taqqu, Murad S.
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Citation (published version)G. Peccati, J.L. Sole, M.S. Taqqu, F. Utzet. 2010. "STEIN'S METHOD AND NORMAL APPROXIMATION OF POISSON FUNCTIONALS." ANNALS OF PROBABILITY, Volume 38, Issue 2, pp. 443 - 478 (36). https://doi.org/10.1214/09-AOP477
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.