Introduction to the Theory of (Non-Symmetric) Dirichlet Forms

1. Front Matter

   Pages i-viii

   PDF

2. Introduction

   • Zhi-Ming Ma, Michael Röckner

   Pages 1-5

3. Functional Analytic Background

   • Zhi-Ming Ma, Michael Röckner

   Pages 7-40

4. Examples

   • Zhi-Ming Ma, Michael Röckner

   Pages 41-69

5. Analytic Potential Theory of Dirichlet Forms

   • Zhi-Ming Ma, Michael Röckner

   Pages 71-86

6. Markov Processes and Dirichlet Forms

   • Zhi-Ming Ma, Michael Röckner

   Pages 87-145

7. Characterization of Particular Processes

   • Zhi-Ming Ma, Michael Röckner

   Pages 147-172

8. Regularization

   • Zhi-Ming Ma, Michael Röckner

   Pages 173-181

9. Back Matter

   Pages 183-212

   PDF

The purpose of this book is to give a streamlined introduction to the theory of (not necessarily symmetric) Dirichlet forms on general state spaces. It includes both the analytic and the probabilistic part of the theory up to and including the construction of an associated Markov process. It is based on recent joint work of S. Albeverio and the two authors and on a one-year-course on Dirichlet forms taught by the second named author at the University of Bonn in 1990/9l. It addresses both researchers and graduate students who require a quick but complete introduction to the theory. Prerequisites are a basic course in probabil­ ity theory (including elementary martingale theory up to the optional sampling theorem) and a sound knowledge of measure theory (as, for example, to be found in Part I of H. Bauer [B 78]). Furthermore, an elementary course on lin­ ear operators on Banach and Hilbert spaces (but without spectral theory) and a course on Markov processes would be helpful though most of the material needed is included here.

• Dirichlet form
• Hunt process
• Markov process
• Potential theory
• Probability theory
• stochastic processes

• Institute of Applied Mathematics, Academia Sinica, Beijing, People’s Republic of China

  Zhi-Ming Ma

• Institut für Angewandte Mathematik, Universität Bonn, Bonn 1, Germany

  Michael Röckner

Policies and ethics