A four moments theorem for Gamma limits on a Poisson chaos

Tobias Fissler, Christoph Thäle

Publication: Scientific journalJournal articlepeer-review


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.
Original languageEnglish
Pages (from-to)163 - 192
Issue number1
Publication statusPublished - 2016

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