文章基本信息

标题：Gamma limits and U -statistics on the Poisson space
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作者：Giovanni Peccati ; Christoph Thäle
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2013
卷号：X
页码：525-560
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Using Stein’s method and the Malliavin calculus of variations, we deriveexplicit estimates for the Gamma approximation of functionals of a Poissonmeasure. In particular, conditions are presented under which the distribution ofa sequence of multiple Wiener-Itˆo stochastic integrals with respect to a compensatedPoisson measure converges to a Gamma distribution. As an illustration, wepresent a quantitative version and a non-central extension of a classical theoremby de Jong in the case of degenerate U-statistics of order two. Several multidimensionalextensions, in particular allowing for mixed or hybrid limit theorems, arealso provided.
关键词：Chaos; Contraction; Gamma distribution; De Jong’s theorem; Malli-;avin calculus; Mixed limit theorem; Multiple stochastic integral; Non-central limit theorem; Pois-;son process; Stein’s method; U-statistic