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...
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| Veröffentlicht in: | The Annals of probability 2012-11, Vol.40 (6), p.2439-2459 |
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| container_title | The Annals of probability |
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| creator | Ledoux, M. |
| description | 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. |
| doi_str_mv | 10.1214/11-aop685 |
| format | Article |
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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | 60F05 60H99 60J35 60J60 60J99 Algebra Chaos Chaos theory Convergence eigenfunction Eigenfunctions Eigenvalues fourth moment Gamma-calculus Gaussian distributions Integration by parts iterated gradient Markov analysis Markov operator Mathematical moments Normal distribution Polynomials Spectral theory Stein’s method Studies |
| title | CHAOS OF A MARKOV OPERATOR AND THE FOURTH MOMENT CONDITION |
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