The Stein-Dirichlet-Malliavin method

TL;DR

This paper enhances Stein's method by integrating Malliavin calculus, creating a functional approach suitable for infinite-dimensional spaces, thus broadening its applicability in probability distribution analysis.

Contribution

It introduces a novel combination of Stein's method with Malliavin calculus, extending its use to infinite-dimensional settings.

Findings

Enriched Stein's method with Malliavin calculus

Developed a functional approach for infinite-dimensional spaces

Provided bounds for distribution distances in complex spaces

Abstract

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.