The fourth moment theorem on the Poisson space
C Döbler, G Peccati - The Annals of Probability, 2018 - JSTOR
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 …
variables belonging to the Wiener chaos of a general Poisson random measure. Such a …
Quantitative de Jong theorems in any dimension
C Döbler, G Peccati - 2017 - projecteuclid.org
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 …
Jong's central limit theorem under optimal conditions, stating that a sequence of Hoeffding …
Fourth moment theorems on the Poisson space in any dimension
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 …
recently proved by C. Döbler and G. Peccati (2017). In particular, by adapting the …
Classical and free fourth moment theorems: universality and thresholds
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 …
that IE X^ 4 ≥ 3 IE X 4≥ 3. Let {F_n:\, n ≥ 1\} F n: n≥ 1 denote a normalized sequence of …
Free quantitative fourth moment theorems on Wigner space
S Bourguin, S Campese - International Mathematics Research …, 2018 - academic.oup.com
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 …
symmetric kernels, generalizing an earlier result from Kemp et al.(2012). The proof relies on …
Poisson convergence on the free Poisson algebra
S Bourguin - 2015 - projecteuclid.org
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) …
for an element of a free Poisson chaos of arbitrary order to converge to a free (centered) …
Universality of free homogeneous sums in every dimension
R Simone - arXiv preprint arXiv:1401.1423, 2014 - arxiv.org
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 …
on freely independent non-commutative random variables of the type $ U_n (S) $, where …
Multidimensional limit theorems for homogeneous sums: a survey and a general transfer principle
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 …
and of universal limit theorems, for multilinear homogeneous sums, in both the classical and …
[PDF][PDF] Recent developments around the Malliavin-Stein approach (Fourth moment phenomena via exchangeable pairs)
G Zheng - 2018 - orbilu.uni.lu
DISSERTATION DOCTEUR DE L’UNIVERSITÉ DU LUXEMBOURG EN MATHEMATIQUES
Guangqu ZHENG Dissertation defence committee Page 1 PhD-FSTC-2018-26 The Faculty of …
Guangqu ZHENG Dissertation defence committee Page 1 PhD-FSTC-2018-26 The Faculty of …
A four moments theorem for gamma limits on a Poisson chaos
T Fissler, C Thäle - arXiv preprint arXiv:1502.01568, 2015 - arxiv.org
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 …
q $ generated by a Poisson random measure on a Polish space. The problem is …