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.

Readership

Graduate students and research mathematicians interested in probability and random processes.