Quantitative stable limit theorems on the Wiener space
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Issue Date
2016Author
Nourdin, Ivan
Nualart, David
Peccati, Giovanni
Publisher
Institute of Mathematical Statistics
Type
Article
Article Version
Scholarly/refereed, publisher version
Rights
© Institute of Mathematical Statistics, 2016
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Show full item recordAbstract
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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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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