@article{EJP3061,
author = {Peter Eichelsbacher and Christoph Thäle},
title = {New Berry-Esseen bounds for non-linear functionals of Poisson random measures},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
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},
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.},
pages = {no. 102, 1-25},
issn = {1083-6489},
doi = {10.1214/EJP.v19-3061},
url = {http://ejp.ejpecp.org/article/view/3061}}