| Autor: |
Nourdin, Ivan, Peccati, Giovanni, Poly, Guillaume, Simone, Rosaria |
| Rok vydání: |
2015 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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