Second order Poincar\'e inequalities and CLTs on Wiener space
Ivan Nourdin (PMA), Giovanni Peccati (MODAL'X), Gesine Reinert
TL;DR
This paper establishes second order Poincaré inequalities on Wiener space, connecting Gaussian limit theorems, Stein's method, and Malliavin calculus, with applications to CLTs and Gaussian-subordinated fields.
Contribution
It introduces second order Poincaré inequalities in infinite-dimensional Wiener space, advancing the theoretical framework for Gaussian limit theorems.
Findings
New characterization of CLTs on Wiener chaos
Application to linear functionals of Gaussian fields
Bridging Stein's method and Malliavin calculus
Abstract
We prove infinite-dimensional second order Poincar\'e inequalities on Wiener space, thus closing a circle of ideas linking limit theorems for functionals of Gaussian fields, Stein's method and Malliavin calculus. We provide two applications: (i) to a new "second order" characterization of CLTs on a fixed Wiener chaos, and (ii) to linear functionals of Gaussian-subordinated fields.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometry and complex manifolds · Stochastic processes and financial applications · Advanced Mathematical Physics Problems