Universal Gaussian fluctuations on the discrete Poisson chaos

Giovanni Peccati (1) , Cengbo Zheng (2, 3)

1 Unité de Recherche en Mathématiques
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We prove that homogenous sums inside a fixed discrete Poisson chaos are universal with respect to normal approximations. This result parallels some recent findings, in a Gaussian context, by Nourdin, Peccati and Reinert (2010). As a by-product of our analysis, we provide some refinements of the CLTs for random variables on the Poisson space proved by Peccati, Solé, Taqqu and Utzet (2010), and by Peccati and Zheng (2010).

Mots clés: Central Limit Theorems; Contractions; Discrete Poisson Chaos; Universality

Domaines: Probabilités [math.PR]

Giovanni Peccati, Cengbo Zheng. Universal Gaussian fluctuations on the discrete Poisson chaos. 2011. ⟨hal-00635769⟩