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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.
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https://hal.archives-ouvertes.fr/hal-00472225
Contributor : Cengbo Zheng Connect in order to contact the contributor
Submitted on : Friday, April 9, 2010 - 6:55:46 PM
Last modification on : Tuesday, November 16, 2021 - 4:59:17 AM
Long-term archiving on: : Tuesday, September 14, 2010 - 6:09:49 PM

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

Citation

Giovanni Peccati, Cengbo Zheng. Multi-dimensional Gaussian fluctuations on the Poisson space. 2010. ⟨hal-00472225⟩

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Les métriques sont temporairement indisponibles