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New Berry-Esseen bounds for non-linear functionals of Poisson random measures


 
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1. Title Title of document New Berry-Esseen bounds for non-linear functionals of Poisson random measures
 
2. Creator Author's name, affiliation, country Peter Eichelsbacher; Ruhr University Bochum; Germany
 
2. Creator Author's name, affiliation, country Christoph Thäle; Ruhr University Bochum; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) 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
 
3. Subject Subject classification Primary 60F05; 60G57; 60G55; Secondary 60H05; 60H07; 60D05; 60G51
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Supported by the German research foundation (DFG) via SFB-TR 12.
 
7. Date (YYYY-MM-DD) 2014-10-28
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3061
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3061
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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