Multidimensional limit theorems for homogeneous sums: 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.
Keywords
Cite
@article{arxiv.1506.07829,
title = {Multidimensional limit theorems for homogeneous sums: a general transfer principle},
author = {Ivan Nourdin and Giovanni Peccati and Guillaume Poly and Rosaria Simone},
journal= {arXiv preprint arXiv:1506.07829},
year = {2015}
}