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

(24 Jun 2009)

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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.


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