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Stochastic Partial Differential Equations

A Modeling, White Noise Functional Approach

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

Part of the Probability and its Applications book series (PA)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang
    Pages 1-10
  3. Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang
    Pages 11-103
  4. Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang
    Pages 105-140
  5. Helge Holden, Bernt Øksendal, Jan Ubøe, Tusheng Zhang
    Pages 141-191
  6. Back Matter
    Pages 193-231

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Helge Holden
    • 1
  • Bernt Øksendal
    • 2
  • Jan Ubøe
    • 3
  • Tusheng Zhang
    • 3
  1. 1.Dept. of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Department of MathematicsUniversity of OsloOsloNorway
  3. 3.Stord/Haugesund CollegeHaugesundNorway

Bibliographic information