CHAOS OF A MARKOV OPERATOR AND THE FOURTH MOMENT CONDITION

• 成果类型: Article
• 署名作者: Ledoux, M.
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Institut Universitaire de France
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP685
• 发表日期: 2012
• 页码: 2439-2459
• 关键词: multiple stochastic integrals; central limit-theorems; steins method; normal approximation; malliavin calculus; functionals

摘要

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.