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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NormalApproximationOfPoissonFunctionalsInKolmogorovDistance.pdf - Accepted Version Available under License Publisher holds Copyright. Download (321kB) | Preview |
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) |
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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: |
05 Dec 2022 15:01 |
Publisher DOI: |
10.1007/s10959-014-0576-6 |
BORIS DOI: |
10.7892/boris.93226 |
URI: |
https://boris.unibe.ch/id/eprint/93226 |