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Pré-Publication, Document De Travail Année : 2016

Stein's method on the second Wiener chaos : 2-Wasserstein distance

Ehsan Azmoodeh
  • Fonction : Auteur
  • PersonId : 977158
Yvik Swan
  • Fonction : Auteur
  • PersonId : 977159

Résumé

In the first part of the paper we use a new Fourier technique to obtain a Stein characterizations for random variables in the second Wiener chaos. We provide the connection between this result and similar conclusions that can be derived using Malliavin calculus. We also introduce a new form of discrepancy which we use, in the second part of the paper, to provide bounds on the 2-Wasserstein distance between linear combinations of independent centered random variables. Our method of proof is entirely original. In particular it does not rely on estimation of bounds on solutions of the so-called Stein equations at the heart of Stein's method. We provide several applications, and discuss comparison with recent similar results on the same topic.

Dates et versions

hal-01278087 , version 1 (23-02-2016)

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Benjamin Arras, Ehsan Azmoodeh, Guillaume Poly, Yvik Swan. Stein's method on the second Wiener chaos : 2-Wasserstein distance. 2016. ⟨hal-01278087⟩
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