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2014 New Berry-Esseen bounds for non-linear functionals of Poisson random measures
Peter Eichelsbacher, Christoph Thäle
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Electron. J. Probab. 19: 1-25 (2014). DOI: 10.1214/EJP.v19-3061


This paper deals with the quantitative normal approximation of non-linear functionals of Poisson random measures, where the quality is measured by the Kolmogorov distance. Combining Stein's method with the Malliavin calculus of variations on the Poisson space, we derive a bound, which is strictly smaller than what is available in the literature. This is applied to sequences of multiple integrals and sequences of Poisson functionals having a finite chaotic expansion. This leads to new Berry-Esseen bounds in a Poissonized version of de Jong's theorem for degenerate U-statistics. Moreover, geometric functionals of intersection processes of Poisson $k$-flats, random graph statistics of the Boolean model and non-linear functionals of Ornstein-Uhlenbeck-Lévy processes are considered.


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Peter Eichelsbacher. Christoph Thäle. "New Berry-Esseen bounds for non-linear functionals of Poisson random measures." Electron. J. Probab. 19 1 - 25, 2014.


Accepted: 28 October 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1307.60066
MathSciNet: MR3275854
Digital Object Identifier: 10.1214/EJP.v19-3061

Primary: 60F05 , 60G55 , 60G57
Secondary: 60D05 , 60G51 , 60H05 , 60H07

Keywords: Berry-Esseen bound , central limit theorem , de Jong's theorem , flat processes , Malliavin calculus , Multiple stochastic integral , Ornstein-Uhlenbeck-L\'evy process , Poisson process , Random graphs , random measure , Stein's method , U-statistics


Vol.19 • 2014
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