The field of Stochastic Partial Differential Equations (SPDEs) is one of the most dynamically developing areas of mathematics. It lies at the cross section of probability, partial differential equations, population biology, and mathematical physics. The field is especially attractive because of its interdisciplinary nature and the enormous richness of current and potential future applications. This volume is a collection of six important topics in SPDEs presented from the viewpoint of distinguished scientists working in the field and related areas. Emphasized are the genesis and applications of SPDEs as well as mathematical theory and numerical methods.
Part 1: SPDE's and Stochastic Modelling: Stochastic partial differential equations: Selected applications in continuum physics by J. Glimm and D. Sharp Measure-valued processes and renormalization of branching particle systems by D. A. Dawson and E. A. Perkins Deterministic and stochastic hydrodynamic equations arising from simple microscopic model systems by G. Giacomin, J. L. Lebowitz, and E. Presutti Transport by incompressible random velocity fields: Simulations & mathematical conjectures by R. A. Carmona and F. Cerou Part 2: Mathematical Theory of SPDE's: An analytic approach to SPDEs by N. V. Krylov Martingale problems for stochastic PDE's by R. Mikulevicius and B. L. Rozovskii Indexes: Notation index Subject index.