The Annals of Probability

Stein’s method and Normal approximation of Poisson functionals

G. Peccati, J. L. Solé, M. S. Taqqu, and F. 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.

Article information

Source
Ann. Probab., Volume 38, Number 2 (2010), 443-478.

Dates
First available in Project Euclid: 9 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1268143523

Digital Object Identifier
doi:10.1214/09-AOP477

Mathematical Reviews number (MathSciNet)
MR2642882

Zentralblatt MATH identifier
1195.60037

Subjects
Primary: 60F05: Central limit and other weak theorems 60G51: Processes with independent increments; Lévy processes 60G60: Random fields 60H05: Stochastic integrals

Keywords
Malliavin calculus Normal approximation Ornstein–Uhlenbeck process Poisson measure Stein’s method Wasserstein distance

Citation

Peccati, G.; Solé, J. L.; Taqqu, M. S.; Utzet, F. Stein’s method and Normal approximation of Poisson functionals. Ann. Probab. 38 (2010), no. 2, 443--478. doi:10.1214/09-AOP477. https://projecteuclid.org/euclid.aop/1268143523


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