Stochastic Partial Differential Equations: Six Perspectives
About this Title
Rene A. Carmona, Princeton University, Princeton, NJ and Boris Rozovskii, University of Southern California, Los Angeles, CA, Editors
Publication: Mathematical Surveys and Monographs
Publication Year 1998: Volume 64
ISBNs: 978-0-8218-2100-8 (print); 978-1-4704-1291-3 (online)
MathSciNet review: MR1661761
MSC (1991): Primary 60-06; Secondary 35-06, 35R60, 60H15
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.
Graduate students and researchers working in probability theory, PDEs, fluid dynamics, turbulence, chaos, particle systems, population biology, nonlinear filtering and financial mathematics.
Table of Contents
Part 1. Stochastic models
- 1. James Glimm and David Sharp – Stochastic partial differential equations: Selected applications in continuum physics [MR 1661762]
- 2. Donald A. Dawson and Edwin A. Perkins – Measure-Valued processes and renormalization of branching particle systems [MR 1661763]
- 3. Giambattista Giacomin, Joel L. Lebowitz and Errico Presutti – Deterministic and stochastic hydrodynamic equations arising from simple microscopic model systems [MR 1661764]
- 4. Rene A. Carmona and Frederic Cerou – Transport by Incompressible random velocity fields: Simula-tions & Mathematical Conjectures [MR 1661765]
Part 2. Mathematical theory
- 5. N. V. Krylov – An analytic approach to SPDE's [MR 1661766]
- 6. R. Mikulevicius and B. L. Rozovskii – Martingale problems for stochastic PDE's [MR 1661767]