2012/10/29 by M. Ledoux · 1 citation
Mathematics · #math.PR
paper · pdf · doi:10.1214/11-aop685
published as Annals of Probability 2012, Vol. 40, No. 6, 2439-2459 · 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)
arxiv created 2012/10/29 · arxiv updated 2012/10/30
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.