The Annals of Probability
- Ann. Probab.
- Volume 44, Number 1 (2016), 1-41.
Quantitative stable limit theorems on the Wiener space
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.
Ann. Probab., Volume 44, Number 1 (2016), 1-41.
Received: May 2013
Revised: August 2014
First available in Project Euclid: 2 February 2016
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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