Fourth moment theorems on the Poisson space: analytic statements via product formulae
Probability
2018-08-07 v1
Abstract
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 carr\'e-du-champ operators. Our results substantially complete the fourth moment theorems recently obtained by D\"obler and Peccati (2018) and D\"obler, Vidotto and Zheng (2018). An important tool for achieving our goals is a novel product formula for multiple integrals under minimal conditions.
Keywords
Cite
@article{arxiv.1808.01836,
title = {Fourth moment theorems on the Poisson space: analytic statements via product formulae},
author = {Christian Döbler and Giovanni Peccati},
journal= {arXiv preprint arXiv:1808.01836},
year = {2018}
}
Comments
14 pages