The Fokker-Planck Equation

1. Front Matter

   Pages I-XIV

   PDF

2. Introduction

   • Hannes Risken

   Pages 1-12

3. Probability Theory

   • Hannes Risken

   Pages 13-31

4. Langevin Equations

   • Hannes Risken

   Pages 32-62

5. Fokker-Planck Equation

   • Hannes Risken

   Pages 63-95

6. Fokker-Planck Equation for One Variable; Methods of Solution

   • Hannes Risken

   Pages 96-132

7. Fokker-Planck Equation for Several Variables; Methods of Solution

   • Hannes Risken

   Pages 133-162

8. Linear Response and Correlation Functions

   • Hannes Risken

   Pages 163-178

9. Reduction of the Number of Variables

   • Hannes Risken

   Pages 179-195

10. Solutions of Tridiagonal Recurrence Relations, Application to Ordinary and Partial Differential Equations

    • Hannes Risken

    Pages 196-228

11. Solutions of the Kramers Equation

    • Hannes Risken

    Pages 229-275

12. Brownian Motion in Periodic Potentials

    • Hannes Risken

    Pages 276-373

13. Statistical Properties of Laser Light

    • Hannes Risken

    Pages 374-413

14. Back Matter

    Pages 414-472

    PDF

One of the central problems synergetics is concerned with consists in the study of macroscopic qualitative changes of systems belonging to various disciplines such as physics, chemistry, or electrical engineering. When such transitions from one state to another take place, fluctuations, i.e., random processes, may play an im­ portant role. Over the past decades it has turned out that the Fokker-Planck equation pro­ vides a powerful tool with which the effects of fluctuations close to transition points can be adequately treated and that the approaches based on the Fokker­ Planck equation are superior to other approaches, e.g., based on Langevin equa­ tions. Quite generally, the Fokker-Planck equation plays an important role in problems which involve noise, e.g., in electrical circuits. For these reasons I am sure that this book will find a broad audience. It pro­ vides the reader with a sound basis for the study of the Fokker-Planck equation and gives an excellent survey of the methods of its solution. The author of this book, Hannes Risken, has made substantial contributions to the development and application of such methods, e.g., to laser physics, diffusion in periodic potentials, and other problems. Therefore this book is written by an experienced practitioner, who has had in mind explicit applications to important problems in the natural sciences and electrical engineering.

• Potential
• Random variable
• computer simulation
• correlation
• differential equation
• diffusion
• eigenvalue
• numerical method
• partial differential equation
• probability
• probability theory
• statistics

• Abteilung für Theoretische Physik, Universität Ulm, Oberer Eselsberg, Ulm, Germany

  Hannes Risken

Policies and ethics