# Stein's method meets Malliavin calculus: a short survey with new estimates

Abstract : We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called Stein's method'' for the Gaussian approximations of probability distributions. Special attention is devoted to establishing explicit connections with the classic method of moments: in particular, we use interpolation techniques in order to deduce some new estimates for the moments of random variables belonging to a fixed Wiener chaos. As an illustration, a class of central limit theorems associated with the quadratic variation of a fractional Brownian motion is studied in detail.
Keywords :
Type de document :
Pré-publication, Document de travail
31 pages. To appear in the book "Recent advances in stochastic dynamics and stochastic analysis",.. 2009
Domaine :

https://hal.archives-ouvertes.fr/hal-00398006
Contributeur : Ivan Nourdin <>
Soumis le : jeudi 17 septembre 2009 - 13:15:44
Dernière modification le : jeudi 16 mars 2017 - 01:07:40
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 13:54:33

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NPsurvey.pdf
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### Identifiants

• HAL Id : hal-00398006, version 2
• ARXIV : 0906.4419

### Citation

Ivan Nourdin, Giovanni Peccati. Stein's method meets Malliavin calculus: a short survey with new estimates. 31 pages. To appear in the book "Recent advances in stochastic dynamics and stochastic analysis",.. 2009. <hal-00398006v2>

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