This textbook offers a compact introduction to Malliavin calculus. It covers recent applications, and includes a self-contained presentation of preliminary material on Brownian motion and stochastic calculus. Accessible to non- experts, graduate students and researchers can use this book to master the core techniques necessary for further study.
The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hörmander's sum of squares theorem but has found a range of applications in stochastic analysis. This book presents the features of Malliavin calculus and discusses its main applications. This second edition includes recent applications in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.