Asymptotic Cram\'er type decomposition for Wiener and Wigner integrals
Operator Algebras
2014-09-05 v1 Probability
Abstract
We investigate generalizations of the Cram\'er theorem. This theorem asserts that a Gaussian random variable can be decomposed into the sum of independent random variables if and only if they are Gaussian. We prove asymptotic counterparts of such decomposition results for multiple Wiener integrals and prove that similar results are true for the (asymptotic) decomposition of the semicircular distribution into free multiple Wigner integrals.
Keywords
Cite
@article{arxiv.1209.2898,
title = {Asymptotic Cram\'er type decomposition for Wiener and Wigner integrals},
author = {Solesne Bourguin and Jean-Christophe Breton},
journal= {arXiv preprint arXiv:1209.2898},
year = {2014}
}