A four moments theorem for Gamma limits on a Poisson chaos

Tobias Fissler, Christoph Thäle

Publikation: Wissenschaftliche FachzeitschriftOriginalbeitrag in FachzeitschriftBegutachtung


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.
Seiten (von - bis)163 - 192
PublikationsstatusVeröffentlicht - 2016