| Issue |
ESAIM: Proc.
Volume 51, October 2015
Modélisation Aléatoire et Statistique - Journées MAS 2014
|
|
|---|---|---|
| Page(s) | 49 - 59 | |
| DOI | https://doi.org/10.1051/proc/201551003 | |
| Published online | 12 October 2015 | |
The Stein-Dirichlet-Malliavin method
Institut Mines-Telecom, Telecom
ParisTech, CNRS LTCI, Paris, France
The Stein’s method is a popular method used to derive upper-bounds of distances between probability distributions. It can be viewed, in certain of its formulations, as an avatar of the semi-group or of the smart-path method used commonly in Gaussian analysis. We show how this procedure can be enriched by Malliavin calculus leading to a functional approach valid in infinite dimensional spaces.
Résumé
La méthode dite de Stein est habituellement utilisée pour évaluer des bornes supérieures de distances entre mesures de probabilité. Nous montrons comment l’une de ses variantes, appelée méthode du semi-groupe peut tre enrichie par le calcul de Malliavin. Cela permet notamment de traiter des exemples dans des espaces fonctionnels de dimension infinie.
© EDP Sciences, SMAI 2015
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