Fourth Moment Theorem and q-Brownian Chaos

Abstract : In 2005, Nualart and Peccati showed the so-called Fourth Moment Theorem asserting that, for a sequence of normalized multiple Wiener-Itô integrals to converge to the standard Gaussian law, it is necessary and sufficient that its fourth moment tends to 3. A few years later, Kemp et al. extended this theorem to a sequence of normalized multiple Wigner integrals, in the context of the free Brownian motion. The q-Brownian motion, q in (-1,1], introduced by the physicists Frisch and Bourret in 1970 and mathematically studied by Bozejko and Speicher in 1991, interpolates between the classical Brownian motion (q=1) and the free Brownian motion (q=0), and is one of the nicest examples of non-commutative processes. The question we shall solve in this paper is the following: what does the Fourth Moment Theorem become when dealing with a q-Brownian motion?
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Communications in Mathematical Physics, Springer Verlag, 2013
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Contributeur : Ivan Nourdin <>
Soumis le : dimanche 12 février 2012 - 17:35:33
Dernière modification le : jeudi 27 avril 2017 - 09:46:42
Document(s) archivé(s) le : dimanche 13 mai 2012 - 02:21:03

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  • HAL Id : hal-00669247, version 1
  • ARXIV : 1202.2545

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Aurélien Deya, Salim Noreddine, Ivan Nourdin. Fourth Moment Theorem and q-Brownian Chaos. Communications in Mathematical Physics, Springer Verlag, 2013. <hal-00669247>

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