Multi-dimensional Gaussian fluctuations on the Poisson space

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.
Document type :
Preprints, Working Papers, ...
40 pages. 2010
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00472225
Contributor : Cengbo Zheng <>
Submitted on : Friday, April 9, 2010 - 6:55:46 PM
Last modification on : Thursday, March 16, 2017 - 1:07:38 AM
Document(s) archivé(s) le : Tuesday, September 14, 2010 - 6:09:49 PM

Files

Pec_Zheng_9AVR010.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00472225, version 1
  • ARXIV : 1004.2175

Collections

Citation

Giovanni Peccati, Cengbo Zheng. Multi-dimensional Gaussian fluctuations on the Poisson space. 40 pages. 2010. <hal-00472225>

Share

Metrics

Record views

117

Document downloads

93