A four moments theorem for Gamma limits on a Poisson chaos

Tobias Fissler; Christoph Thaele

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arXiv · 1502.01568

A four moments theorem for Gamma limits on a Poisson chaos

Tobias Fissler·Christoph Thaele

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Abstract

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.

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BibTeX RIS

Tobias Fissler, Christoph Thaele. 2015-02-05. A four moments theorem for Gamma limits on a Poisson chaos. https://arxiv.org/abs/1502.01568

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