Normal approximation of Poisson functionals in Kolmogorov distance

Schulte, Matthias (2016). Normal approximation of Poisson functionals in Kolmogorov distance. Journal of theoretical probability, 29(1), pp. 96-117. Springer 10.1007/s10959-014-0576-6

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Peccati, Solè, Taqqu, and Utzet recently combined Stein’s method and Malliavin calculus to obtain a bound for the Wasserstein distance of a Poisson functional and a Gaussian random variable. Convergence in the Wasserstein distance always implies convergence in the Kolmogorov distance at a possibly weaker rate. But there are many examples of central limit theorems having the same rate for both distances. The aim of this paper was to show this behavior for a large class of Poisson functionals, namely so-called U-statistics of Poisson point processes. The technique used by Peccati et al. is modified to establish a similar bound for the Kolmogorov distance of a Poisson functional and a Gaussian random variable. This bound is evaluated for a U-statistic, and it is shown that the resulting expression is up to a constant the same as it is for the Wasserstein distance.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Schulte, Matthias

Subjects:

500 Science > 510 Mathematics

ISSN:

0894-9840

Publisher:

Springer

Language:

English

Submitter:

David Ginsbourger

Date Deposited:

25 Apr 2017 11:30

Last Modified:

15 May 2017 09:02

Publisher DOI:

10.1007/s10959-014-0576-6

BORIS DOI:

10.7892/boris.93226

URI:

https://boris.unibe.ch/id/eprint/93226

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