Fourth moment theorems on the Poisson space: analytic statements via product formulae

Electronic Communications in Probability

Christian Döbler¹ 

关键词: multiple Wiener-Itô integrals;    Poisson functionals;    product formula;    fourth moment theorem;    carré-du-champ operator;    Berry-Esseen bounds;    Gaussian approximation;    Malliavin calculus;    Stein’s method;   

DOI  :  10.1214/18-ECP196

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

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.

【 授权许可】

CC BY