Open Access
Translator Disclaimer
January 2016 Quantitative stable limit theorems on the Wiener space
Ivan Nourdin, David Nualart, Giovanni Peccati
Ann. Probab. 44(1): 1-41 (January 2016). DOI: 10.1214/14-AOP965

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.

Citation

Download Citation

Ivan Nourdin. David Nualart. Giovanni Peccati. "Quantitative stable limit theorems on the Wiener space." Ann. Probab. 44 (1) 1 - 41, January 2016. https://doi.org/10.1214/14-AOP965

Information

Received: 1 May 2013; Revised: 1 August 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 1356.60035
MathSciNet: MR3456331
Digital Object Identifier: 10.1214/14-AOP965

Subjects:
Primary: 60F05, 60G15, 60H07

Rights: Copyright © 2016 Institute of Mathematical Statistics

JOURNAL ARTICLE
41 PAGES


SHARE
Vol.44 • No. 1 • January 2016
Back to Top