Publisher's Synopsis
The book discusses the following topics in stochastic analysis: 1. Stochastic analysis related to Lie groups: stochastic analysis of loop spaces and infinite dimensional manifolds has been developed rapidly after the fundamental works of Gross and Malliavin. (Lectures by Driver, Gross, Mitoma, and Sengupta.);2. Stochastic partial differential equations: Linear and quasi-linear equations with initial conditions (or terminal conditions) and boundary conditions have been studied extensively in recent years. (Lectures by Chow, Kallianpur, Kunita, Nisio, Pitt, and Rozovskii.);3. Stochastic flows and analysis on Wiener functionals: these two objects cooperate well and produce a theory on generalized Wiener functionals through the works of Kunita and Watanabe. (Lectures by Kunita, Protter, Shigekawa, and S. Watanabe.);4. Large deviations: large deviations for stochastic processes arising from branching processes and for measure-valued stochastic differential equations. (Lectures by Funaki, Gorostiza, Ney, and Varadhan.);5. White noise calculus: white noise calculus is an infinite dimensional distribution theory. It provides new tools for stochastic integration and mathematical physics, etc. (Lectures by Hida, Kubo, Kuo, Lee, Redfern, and Streit.);6. Stable laws: Stable laws on Banach spaces and their applications. (Lectures by Mandrekar, Rajput, Rosinski, and H. Sato.)
