期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2016
卷号：XIII
页码：163-192
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：This paper deals with sequences of random variables belonging to a xed 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 momentof such a suitably normalized sequence to the third and fourth moment of a centredGamma 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 momentstheorem is based on a number of new estimates for contraction norms. Applicationsconcern homogeneous sums and U-statistics on the Poisson space.
