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

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

2009-06-24

arxiv.org/abs/0906.4419v2

Mathematics

Probability

31 pages. To appear in the book "Recent advances in stochastic dynamics and stochastic analysis", published by World Scientifi

Scientific paper

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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