Paul Malliavin developed the stochastic calculus of variations that bears his name in 1976 primarily to establish the regularity of the probability distribution of functionals of an underlying Gaussian process. Since then it has proven to be a powerful tool for a variety of problems in stochastic analysis. Nualart has prepared this monograph from his notes for ten lectures he delivered at the conference, held at Kent State University, Ohio, in August 2008. In order to demonstrate applications, he concentrates on a Gaussian family of random variables associated with an arbitrary separable Hilbert space. Some of the examples are barely mentioned, but he provides full references for readers who want more. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)