Multi-Dimensional Gaussian Fluctuations on the Poisson Space

By Giovanni Peccati, Cengbo Zheng. 2010

81 citations recorded by the source corpus.

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, Sole, Taqqu and Utzet. Several explicit examples (including in particular vectors of linear and non-linear functionals of Ornstein-Uhlenbeck Levy processes) are discussed in detail.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/329e5d59d8aa7c9f208d62c8c9cec13fe4798ad6

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Citations in the corpus

Central limit theorems for $U$-statistics of Poisson point processes (2011, methodology): “Further developments include the book of Peccati and Taqqu [28] about product formulas for multiple Wiener–Itô integrals in the Gaussian and Poisson case and a central limit theorem due to Peccati and Zheng [29] generalizing the main result of [27] to random vectors.”
Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs (2011, methodology): “These analytic objects already appear in CLTs living inside a fixed Wiener chaos (see [25, 26]), and are a crucial tool in order to effectively assess bounds based on Malliavin operators.”
Second-order properties and central limit theorems for geometric functionals of Boolean models (2013, methodology): “In the proofs we use the Malliavin-Stein method for Poisson functionals that was recently developed in [21, 23].”