Optimal Berry-Esseen bounds on the Poisson space
Probability
2015-05-13 v2
Abstract
We establish new lower bounds for the normal approximation in the Wasserstein distance of random variables that are functionals of a Poisson measure. Our results generalize previous findings by Nourdin and Peccati (2012, 2015) and Bierm\'e, Bonami, Nourdin and Peccati (2013), involving random variables living on a Gaussian space. Applications are given to optimal Berry-Esseen bounds for edge counting in random geometric graphs.
Cite
@article{arxiv.1505.02578,
title = {Optimal Berry-Esseen bounds on the Poisson space},
author = {Ehsan Azmoodeh and Giovanni Peccati},
journal= {arXiv preprint arXiv:1505.02578},
year = {2015}
}