Universal Gaussian fluctuations on the discrete Poisson chaos

Details Universal Gaussian fluctuations on the discrete Poisson chaos Universal Gaussian fluctuations on the discrete Poisson chaos

2011-10-26

arxiv.org/abs/1110.5723v1

Mathematics

Probability

18 pages

Scientific paper

We prove that homogenous sums inside a fixed discrete Poisson chaos are universal with respect to normal approximations. This result parallels some recent findings, in a Gaussian context, by Nourdin, Peccati and Reinert (2010). As a by-product of our analysis, we provide some refinements of the CLTs for random variables on the Poisson space proved by Peccati, Sol\'e, Taqqu and Utzet (2010), and by Peccati and Zheng (2010).

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