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arXiv · 1505.02578

Optimal Berry-Esseen bounds on the Poisson space

Ehsan Azmoodeh·Giovanni Peccati
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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 Biermé, 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.

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Ehsan Azmoodeh, Giovanni Peccati. 2015-05-12. Optimal Berry-Esseen bounds on the Poisson space. https://arxiv.org/abs/1505.02578

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