The Annals of Probability
- Ann. Probab.
- Volume 40, Number 6 (2012), 2439-2459.
Chaos of a Markov operator and the fourth moment condition
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.
Ann. Probab., Volume 40, Number 6 (2012), 2439-2459.
First available in Project Euclid: 26 October 2012
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Primary: 60F05: Central limit and other weak theorems 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 60J60: Diffusion processes [See also 58J65] 60J99: None of the above, but in this section 60H99: None of the above, but in this section
Ledoux, M. Chaos of a Markov operator and the fourth moment condition. Ann. Probab. 40 (2012), no. 6, 2439--2459. doi:10.1214/11-AOP685. https://projecteuclid.org/euclid.aop/1351258731