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

@article{citeulike:4952137, 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.}, archivePrefix = {arXiv}, author = {Nourdin, Ivan and Peccati, Giovanni}, citeulike-article-id = {4952137}, citeulike-linkout-0 = {http://arxiv.org/abs/0906.4419}, citeulike-linkout-1 = {http://arxiv.org/pdf/0906.4419}, day = {24}, eprint = {0906.4419}, keywords = {malliavin, stein-method, wiener-chaos}, month = {Jun}, posted-at = {2009-06-25 08:35:40}, priority = {2}, title = {Stein's method meets Malliavin calculus: a short survey with new estimates}, url = {http://arxiv.org/abs/0906.4419}, year = {2009} }

TY - JOUR ID - citeulike:4952137 L3 - citeulike-article-id:4952137 N2 - 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. TI - Stein's method meets Malliavin calculus: a short survey with new estimates KW - malliavin KW - stein-method KW - wiener-chaos AU - Nourdin, Ivan AU - Peccati, Giovanni PY - 2009/Jun/24/ UR - http://arxiv.org/abs/0906.4419 ER -