Reference : A Peccati-Tudor type theorem for Rademacher chaoses
E-prints/Working papers : Already available on another site
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/32843
A Peccati-Tudor type theorem for Rademacher chaoses
English
Zheng, Guangqu mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2017
Yes
[en] fourth moment theorem ; maximal influence ; exchangeable pairs
[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.
Researchers ; Students
http://hdl.handle.net/10993/32843
https://arxiv.org/abs/1708.05283

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
PT-Rad.pdfAuthor preprint182.2 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.