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.

Readership

Graduate students and researchers working in probability theory, PDEs, fluid dynamics, turbulence, chaos, particle systems, population biology, nonlinear filtering and financial mathematics.

Reviews

"The different chapters are independent of each other and are all accessible to the reader with reasonable notions of analysis and stochastic integration. This collection of monographs can strongly stimulate the interest of readers, and motivate them to read more specialized books and articles."

-- Journal of the American Statistical Association

Table of Contents

• J. Glimm and D. Sharp -- Stochastic partial differential equations: Selected applications in continuum physics
• D. A. Dawson and E. A. Perkins -- Measure-valued processes and renormalization of branching particle systems
• G. Giacomin, J. L. Lebowitz, and E. Presutti -- Deterministic and stochastic hydrodynamic equations arising from simple microscopic model systems
• R. A. Carmona and F. Cerou -- Transport by incompressible random velocity fields: Simulations & mathematical conjectures

• N. V. Krylov -- An analytic approach to SPDEs
• R. Mikulevicius and B. L. Rozovskii -- Martingale problems for stochastic PDE's

• Notation index
• Subject index