Chaos of a Markov operator and the fourth moment condition

• Autores: M. Ledoux
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 40, Nº. 6, 2012, págs. 2439-2459
• Idioma: inglés
• DOI: 10.1214/11-AOP685
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.