Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach

✍ Scribed by Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang (auth.)

• Publisher: Birkhäuser Basel
• Year: 1996
• Tongue: English
• Leaves: 238
• Series: Probability and its Applications
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction....Pages 1-10
Framework....Pages 11-103
Applications to stochastic ordinary differential equations....Pages 105-140
Stochastic partial differential equations....Pages 141-191
Back Matter....Pages 193-231

✦ Subjects

Probability Theory and Stochastic Processes; Partial Differential Equations; Theoretical, Mathematical and Computational Physics