Multidimensional limit theorems for homogeneous sums: a survey and a general transfer principle - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Probability and Statistics Year : 2016

Multidimensional limit theorems for homogeneous sums: a survey and a general transfer principle

Abstract

The aim of the present paper is to establish the multidimensional counterpart of the \textit{fourth moment criterion} for homogeneous sums in independent leptokurtic and mesokurtic random variables (that is, having positive and zero fourth cumulant, respectively), recently established in \cite{NPPS} in both the classical and in the free setting. As a consequence, the transfer principle for the Central limit Theorem between Wiener and Wigner chaos can be extended to a multidimensional transfer principle between vectors of homogeneous sums in independent commutative random variables with zero third moment and with non-negative fourth cumulant, and homogeneous sums in freely independent non-commutative random variables with non-negative fourth cumulant.

Dates and versions

hal-01171866 , version 1 (06-07-2015)

Identifiers

Cite

Ivan Nourdin, Giovanni Peccati, Guillaume Poly, Rosaria Simone. Multidimensional limit theorems for homogeneous sums: a survey and a general transfer principle. ESAIM: Probability and Statistics, 2016, 20, pp.293-308. ⟨10.1051/ps/2016014⟩. ⟨hal-01171866⟩
112 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More