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2010 Multi-Dimensional Gaussian Fluctuations on the Poisson Space
Peccati Giovanni, Cengbo Zheng
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Electron. J. Probab. 15: 1487-1527 (2010). DOI: 10.1214/EJP.v15-813

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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Peccati Giovanni. Cengbo Zheng. "Multi-Dimensional Gaussian Fluctuations on the Poisson Space." Electron. J. Probab. 15 1487 - 1527, 2010. https://doi.org/10.1214/EJP.v15-813

Information

Accepted: 15 October 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1228.60031
MathSciNet: MR2727319
Digital Object Identifier: 10.1214/EJP.v15-813

Subjects:
Primary: 60F05
Secondary: 60G51, 60G57, 60H05, 60H07

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Vol.15 • 2010
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