The Annals of Probability

Quantitative stable limit theorems on the Wiener space

Ivan Nourdin, David Nualart, and Giovanni Peccati

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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.

Article information

Source
Ann. Probab., Volume 44, Number 1 (2016), 1-41.

Dates
Received: May 2013
Revised: August 2014
First available in Project Euclid: 2 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1454423034

Digital Object Identifier
doi:10.1214/14-AOP965

Mathematical Reviews number (MathSciNet)
MR3456331

Zentralblatt MATH identifier
1356.60035

Subjects
Primary: 60F05: Central limit and other weak theorems 60H07: Stochastic calculus of variations and the Malliavin calculus 60G15: Gaussian processes

Keywords
Stable convergence Malliavin calculus fractional Brownian motion

Citation

Nourdin, Ivan; Nualart, David; Peccati, Giovanni. Quantitative stable limit theorems on the Wiener space. Ann. Probab. 44 (2016), no. 1, 1--41. doi:10.1214/14-AOP965. https://projecteuclid.org/euclid.aop/1454423034


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