Stochastic Analysis on Infinite Dimensional Spaces

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.)