Stochastic analysis

Stochastic analysis is the analysis of functionals defined on the Wiener space, i.e., the space on which a Wiener process is realized. Since the Wiener space is infinite-dimensional, it requires a special calculus, the so-called Malliavin calculus. The goal of the book is to provide the reader with a concise introduction to stochastic analysis, and, in particular, to the Malliavin calculus. The book contains a detailed description of all technical tools necessary to describe the theory, such as the Wiener process, the Ornstein-Uhlenbeck process, and Sobolev spaces. It also presents applications of stochastic calculus to the study of stochastic differential equations.