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.