The Malliavin Calculus and Related Topics (Probability and its Applications)
The Malliavin Calculus and Related Topics (Probability and its Applications)
ISBN: 9783540283287
出版社: Springer
出版年: 2006-02-10
页数: 382
定价: USD 89.95
装帧: Hardcover
内容简介
The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on a Gaussian space. Originally, it was developed to provide a probabilistic proof to H?rmander's "sum of squares" theorem, but it has found a wide range of applications in stochastic analysis. This monograph presents the main features of the Malliavin calculus and discusses in detail its main applications. The author begins by developing the analysis on the Wiener space, and then uses this to establish the regularity of probability laws and to prove H?rmander's theorem. The regularity of the law of stochastic partial differential equations driven by a space-time white noise is also studied. The subsequent chapters develop the connection of the Malliavin with the anticipating stochastic calculus, studying anticipating stochastic differential equations and the Markov property of solutions to stochastic differential equations with boundary conditions. The second edition of this monograph includes recent applications of the Malliavin calculus in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.