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A Peccati-Tudor type theorem for Rademacher chaoses
Zheng, Guangqu


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Keywords :
fourth moment theorem; maximal influence; exchangeable pairs
Abstract :
[en] In this article, we prove that in the Rademacher setting, a random vector with chaotic components is close in distribution to a centred Gaussian vector, if both the maximal influence of the associated kernel and the fourth cumulant of each component is small. In particular, we recover the univariate case recently established in D\"obler and Krokowski (2017). Our main strategy consists in a novel adaption of the exchangeable pairs couplings initiated in Nourdin and Zheng (2017), as well as its combination with estimates via chaos decomposition.
Disciplines :
Author, co-author :
Zheng, Guangqu ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
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Title :
A Peccati-Tudor type theorem for Rademacher chaoses
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