Stochastic Partial Differential Equations

1. Front Matter

   Pages i-xii

   PDF

2. Introduction

   • Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang

   Pages 1-10

3. Framework

   • Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang

   Pages 11-103

4. Applications to stochastic ordinary differential equations

   • Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang

   Pages 105-140

5. Stochastic partial differential equations

   • Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang

   Pages 141-191

6. Back Matter

   Pages 193-231

   PDF

This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera­ tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre­ sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in reservoir theory and related areas. 3) The theory should be strong and efficient enough to allow us to solve th,~se SPDEs explicitly, or at least provide algorithms or approximations for the solutions.

• Equations
• Mathematics
• algorithms
• calculus
• chaos
• differential equation
• mathematics
• model
• modeling
• numerical simulation
• ordinary differential equation
• Parameter
• partial differential equation
• Schrödinger equation
• solution
• stochastic differential equation
• Variance
• partial differential equations

"The authors have made significant contributions to each of the areas. As a whole, the book is well organized and very carefully written and the details of the proofs are basically spelled out... This is a rich and demanding book… It will be of great value for students of probability theory or SPDEs with an interest in the subject, and also for professional probabilists."   —Mathematical Reviews

"...a comprehensive introduction to stochastic partial differential equations."   —Zentralblatt MATH

"This book will be invaluable to anyone interested in doing research in white noise theory or in applying this theory to solving real-world problems."   —Computing Reviews

• Dept. of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

  Helge Holden

• Department of Mathematics, University of Oslo, Oslo, Norway

  Bernt Øksendal

• Stord/Haugesund College, Haugesund, Norway

  Jan Ubøe, Tusheng Zhang

Policies and ethics