In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-contained and readable exposition by leading authors, provides a rigorous account of the subject, emphasizing the "explicit" rather than the "concise" where necessary, and addressed to readers interested in probability theory as applied to analysis and mathematical physics. A distinctive feature of the methods used is the ubiquitous appearance of stopping time. The book contains much original research by the authors (some of which published...
In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-...
This is a substantial expansion of the first edition. The last chapter on stochastic differential equations is entirely new, as is the longish section 9.4 on the Cameron-Martin-Girsanov formula. Illustrative examples in Chapter 10 include the warhorses attached to the names of L. S. Ornstein, Uhlenbeck and Bessel, but also a novelty named after Black and Scholes. The Feynman-Kac-Schrooinger development (6.4) and the material on re- flected Brownian motions (8.5) have been updated. Needless to say, there are scattered over the text minor improvements and corrections to the first edition. A...
This is a substantial expansion of the first edition. The last chapter on stochastic differential equations is entirely new, as is the longish section...
