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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


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.


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Ivan Nourdin. David Nualart. Giovanni Peccati. "Quantitative stable limit theorems on the Wiener space." Ann. Probab. 44 (1) 1 - 41, January 2016.


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

Primary: 60F05 , 60G15 , 60H07

Keywords: fractional Brownian motion , Malliavin calculus , stable convergence

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 1 • January 2016
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