Chaos of a Markov operator and the fourth moment condition
Probability
2012-10-30 v1
Abstract
We analyze from the viewpoint of an abstract Markov operator recent results by Nualart and Peccati, and Nourdin and Peccati, on the fourth moment as a condition on a Wiener chaos to have a distribution close to Gaussian. In particular, we are led to introduce a notion of chaos associated to a Markov operator through its iterated gradients and present conditions on the (pure) point spectrum for a sequence of chaos eigenfunctions to converge to a Gaussian distribution. Convergence to gamma distributions may be examined similarly.
Keywords
Cite
@article{arxiv.1210.7587,
title = {Chaos of a Markov operator and the fourth moment condition},
author = {M. Ledoux},
journal= {arXiv preprint arXiv:1210.7587},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AOP685 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)