Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 23 (2018), paper no. 91, 12 pp.
Fourth moment theorems on the Poisson space: analytic statements via product formulae
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.
Electron. Commun. Probab., Volume 23 (2018), paper no. 91, 12 pp.
Received: 9 August 2018
Accepted: 16 November 2018
First available in Project Euclid: 15 December 2018
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Döbler, Christian; Peccati, Giovanni. Fourth moment theorems on the Poisson space: analytic statements via product formulae. Electron. Commun. Probab. 23 (2018), paper no. 91, 12 pp. doi:10.1214/18-ECP196. https://projecteuclid.org/euclid.ecp/1544843114