Open Access
Translator Disclaimer
2018 Fourth moment theorems on the Poisson space: analytic statements via product formulae
Christian Döbler, Giovanni Peccati
Electron. Commun. Probab. 23: 1-12 (2018). DOI: 10.1214/18-ECP196


We prove necessary and sufficient conditions for the asymptotic normality of multiple integrals with respect to a Poisson measure on a general measure space, expressed both in terms of norms of contraction kernels and of variances of carré-du-champ operators. Our results substantially complete the fourth moment theorems recently obtained by Döbler and Peccati (2018) and Döbler, Vidotto and Zheng (2018). An important tool for achieving our goals is a novel product formula for multiple integrals under minimal conditions.


Download Citation

Christian Döbler. Giovanni Peccati. "Fourth moment theorems on the Poisson space: analytic statements via product formulae." Electron. Commun. Probab. 23 1 - 12, 2018.


Received: 9 August 2018; Accepted: 16 November 2018; Published: 2018
First available in Project Euclid: 15 December 2018

zbMATH: 07023477
MathSciNet: MR3896829
Digital Object Identifier: 10.1214/18-ECP196

Primary: 60F05 , 60H05 , 60H07

Keywords: Berry-Esseen bounds , carré-du-champ operator , Fourth moment theorem , Gaussian approximation , Malliavin calculus , multiple Wiener-Itô integrals , Poisson functionals , product formula , Stein’s method


Back to Top