We prove a fourth moment bound without remainder for the normal approximation of random
variables belonging to the Wiener chaos of a general Poisson random measure. Such a …

We develop a new quantitative approach to a multidimensional version of the well-known de
Jong's central limit theorem under optimal conditions, stating that a sequence of Hoeffding …

We extend to any dimension the quantitative fourth moment theorem on the Poisson setting,
recently proved by C. Döbler and G. Peccati (2017). In particular, by adapting the …

Let XX be a centered random variable with unit variance and zero third moment, and such
that IE X^ 4 ≥ 3 IE X 4≥ 3. Let {F_n:\, n ≥ 1\} F n: n≥ 1 denote a normalized sequence of …

We prove a quantitative fourth moment theorem for Wigner integrals of any order with
symmetric kernels, generalizing an earlier result from Kemp et al.(2012). The proof relies on …

Based on recent findings by Bourguin and Peccati, we give a fourth moment type condition
for an element of a free Poisson chaos of arbitrary order to converge to a free (centered) …

We prove a general multidimensional invariance principle for a family of U-statistics based
on freely independent non-commutative random variables of the type $ U_n (S) $, where …

We provide a synthetic yet comprehensive review of the so-called fourth moment criterion,
and of universal limit theorems, for multilinear homogeneous sums, in both the classical and …

DISSERTATION DOCTEUR DE L’UNIVERSITÉ DU LUXEMBOURG EN MATHEMATIQUES
Guangqu ZHENG Dissertation defence committee Page 1 PhD-FSTC-2018-26 The Faculty of …

This paper deals with sequences of random variables belonging to a fixed chaos of order $
q $ generated by a Poisson random measure on a Polish space. The problem is …