Multi-dimensional Gaussian fluctuations on the Poisson space

2010/04/13 by Giovanni Peccati, Peccati, Giovanni, Cengbo Zheng +1 · 3 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1004.2175

openalex publication_date 2010/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Chaos, concentration, and multiple valleys

Cited by

• A Kolmogorov fourth-moment bound on Poisson chaos via a martingale core
• Spherical Poisson Needlets with Shrinking Bandwidth
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Related

• Stein's method and normal approximation of Poisson functionals
• Multi-Dimensional Normal Approximation of Heavy-Tailed Moving Averages
• Lectures on Gaussian approximations with Malliavin calculus
• Malliavin-Stein method for multi-dimensional U-statistics of Poisson point processes
• Functional Gaussian approximations on Hilbert-Poisson spaces