Title
Normal Approximations with Malliavin Calculus: From Stein's Method to Universality (Cambridge Tracts in Mathematics, Series Numb,New
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Stein's method is a collection of probabilistic techniques that allow one to assess the distance between two probability distributions by means of differential operators. In 2007, the authors discovered that one can combine Stein's method with the powerful Malliavin calculus of variations, in order to deduce quantitative central limit theorems involving functionals of general Gaussian fields. This book provides an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space. Many recent developments and applications are studied in detail, for instance: fourth moment theorems on the Wiener chaos, density estimates, BreuerMajor theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely selfcontained, the book is perfect for selfstudy. It will appeal to researchers and graduate students in probability and statistics, especially those who wish to understand the connections between Stein's method and Malliavin calculus.
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