A four moments theorem for Gamma limits on a Poisson chaos
Data(s) |
2016
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Resumo |
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. |
Formato |
application/pdf application/pdf |
Identificador |
http://boris.unibe.ch/84023/1/13-07.pdf http://boris.unibe.ch/84023/8/1502.01568v1.pdf 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 doi:10.7892/boris.84023 urn:issn:1980-0436 |
Idioma(s) |
eng |
Publicador |
Institute of Mathematical Statistics |
Relação |
http://boris.unibe.ch/84023/ http://alea.impa.br/articles/v13/13-07.pdf |
Direitos |
info:eu-repo/semantics/restrictedAccess info:eu-repo/semantics/openAccess |
Fonte |
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 |
Palavras-Chave | #510 Mathematics |
Tipo |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion PeerReviewed |