Stein's method and normal approximation of poisson functionals

G. Peccati; J. L. Solé; F. Utzet; M. S. Taqqu

doi:10.1214/09-AOP477

Stein's method and normal approximation of poisson functionals

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

Departament de Matemàtiques

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Resum

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 multipleWiener-Itô integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck Lévy processes.

Idioma original	Anglès
Pàgines (de-a)	443-478
Revista	Annals of Probability
Volum	38
Número	2
DOIs	https://doi.org/10.1214/09-AOP477
Estat de la publicació	Publicada - 1 de març 2010

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title = "Stein's method and normal approximation of poisson functionals",

abstract = "We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Ess{\'e}en bounds in Central limit theorems (CLTs) involving multipleWiener-It{\^o} integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck L{\'e}vy processes.",

keywords = "Malliavin calculus, Normal approximation, Ornstein-uhlenbeck process, Poisson measure, Stein's method, Wasserstein distance.",

author = "G. Peccati and Sol{\'e}, \{J. L.\} and F. Utzet and Taqqu, \{M. S.\}",

year = "2010",

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doi = "10.1214/09-AOP477",

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T1 - Stein's method and normal approximation of poisson functionals

AU - Peccati, G.

AU - Solé, J. L.

AU - Utzet, F.

AU - Taqqu, M. S.

PY - 2010/3/1

Y1 - 2010/3/1

N2 - 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 multipleWiener-Itô integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck Lévy processes.

AB - 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 multipleWiener-Itô integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck Lévy processes.

KW - Malliavin calculus

KW - Normal approximation

KW - Ornstein-uhlenbeck process

KW - Poisson measure

KW - Stein's method

KW - Wasserstein distance.

UR - https://www.scopus.com/pages/publications/77953608052

U2 - 10.1214/09-AOP477

DO - 10.1214/09-AOP477

M3 - Article

SN - 0091-1798

VL - 38

SP - 443

EP - 478

JO - Annals of Probability

JF - Annals of Probability

IS - 2

ER -

Stein's method and normal approximation of poisson functionals

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