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This book explores several aspects of fractional Brownian motion, including the stochastic integration, the study of its supremum and its appearance as limit of partial sums involving stationary sequences.

This book explores several aspects of fractional Brownian motion, including the stochastic integration, the study of its supremum and its appearance as limit of partial sums involving stationary sequences.

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...