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

	Text 13-07.pdf - Published Version Restricted to registered users only Available under License Publisher holds Copyright. Download (531kB)
Preview	Text 1502.01568v1.pdf - Accepted Version Available under License Publisher holds Copyright. Download (331kB) | Preview

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.

Interest & Impact

Downloads

256 since deposited on 20 Jul 2016
14 in the past 12 months

Citations

5 Citations in Web of Science ®
6 Citations in Scopus

Search

in Google Scholar™

Services

Actions (login required)

Edit item

Actions (login required)

Edit item