A four moments theorem for Gamma limits on a Poisson chaos

Fissler, Tobias; Thäle, Christoph (2016). A four moments theorem for Gamma limits on a Poisson chaos. Alea -Latin American journal of probability and mathematical statistics, 13(1), pp. 163-192. Institute of Mathematical Statistics

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Fissler, Tobias

Subjects:

500 Science > 510 Mathematics

ISSN:

1980-0436

Publisher:

Institute of Mathematical Statistics

Language:

English

Submitter:

David Ginsbourger

Date Deposited:

20 Jul 2016 11:00

Last Modified:

21 Jul 2016 05:07

ArXiv ID:

1502.01568

BORIS DOI:

10.7892/boris.84023

URI:

https://boris.unibe.ch/id/eprint/84023

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