Quantitative stable limit theorems on the Wiener space

TL;DR

This paper develops quantitative stable limit theorems on the Wiener space using Malliavin calculus, extending previous results to multidimensional Gaussian mixtures and applying to fractional Brownian motion functionals.

Contribution

It introduces new techniques for stable limit theorems on Wiener space, generalizing prior work and handling multidimensional Gaussian mixtures.

Findings

Refined limit theorems for quadratic functionals

Applications to weighted quadratic variations of fractional Brownian motion

Enhanced understanding of convergence rates in Wiener space

Abstract

We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize previous works by Nourdin and Nualart [J. Theoret. Probab. 23 (2010) 39-64] and Harnett and Nualart [Stochastic Process. Appl. 122 (2012) 3460-3505], and provide a substantial contribution to a recent line of research, focussing on limit theorems on the Wiener space, obtained by means of the Malliavin calculus of variations. Applications are given to quadratic functionals and weighted quadratic variations of a fractional Brownian motion.