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arXiv · 1210.7587

Chaos of a Markov operator and the fourth moment condition

M. Ledoux
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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.

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M. Ledoux. 2012-10-29. Chaos of a Markov operator and the fourth moment condition. https://doi.org/10.1214/11-aop685

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