Quotation Fissler, Tobias, Thäle, Christoph. 2016. A four moments theorem for Gamma limits on a Poisson chaos. Alea. 13 (1), 163-192.




This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space.The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.


Press 'enter' for creating the tag

Publication's profile

Status of publication Published
Affiliation External
Type of publication Journal article
Journal Alea
Citation Index SCI
WU-Journal-Rating new FIN-A
Language English
Title A four moments theorem for Gamma limits on a Poisson chaos
Volume 13
Number 1
Year 2016
Page from 163
Page to 192
URL http://alea.impa.br/articles/v13/13-07.pdf
DOI na
Open Access Y


Fissler, Tobias (Details)
Thäle, Christoph (Ruhr-University Bochum, Germany)
Google Scholar: Search