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Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications

  • Book
  • © 1999

Overview

Authors:
  1. Johan Grasman

    1. Department of Mathematics, Agricultural University, Wageningen, The Netherlands

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    You can also search for this author in PubMed   Google Scholar

  2. Onno A. Herwaarden

    1. Department of Mathematics, Agricultural University, Wageningen, The Netherlands

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    You can also search for this author in PubMed   Google Scholar

  • This is probably the first monograph that treats the asympotic methods which are eminently important for practical applications
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Synergetics (SSSYN)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-IX
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  2. The Fokker—Planck Equation

    1. Front Matter

      Pages 1-1
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    2. Dynamical Systems Perturbed by Noise: the Langevin Equation

      • Johan Grasman, Onno A. van Herwaarden
      Pages 3-17

    3. The Fokker—Planck Equation: First Exit from a Domain

      • Johan Grasman, Onno A. van Herwaarden
      Pages 18-26

    4. The Fokker—Planck Equation: One Dimension

      • Johan Grasman, Onno A. van Herwaarden
      Pages 27-39

  3. Asymptotic Solution of the Exit Problem

    1. Front Matter

      Pages 41-41
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    2. Singular Perturbation Analysis of the Differential Equations for the Exit Probability and Exit Time in One Dimension

      • Johan Grasman, Onno A. van Herwaarden
      Pages 43-72

    3. The Fokker—Planck Equation in Several Dimensions: the Asymptotic Exit Problem

      • Johan Grasman, Onno A. van Herwaarden
      Pages 73-96

  4. Applications

    1. Front Matter

      Pages 97-97
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    2. Dispersive Groundwater Flow and Pollution

      • Johan Grasman, Onno A. van Herwaarden
      Pages 99-117

    3. Extinction in Systems of Interacting Biological Populations

      • Johan Grasman, Onno A. van Herwaarden
      Pages 118-148

    4. Stochastic Oscillation

      • Johan Grasman, Onno A. van Herwaarden
      Pages 149-167

    5. Confidence Domain, Return Time and Control

      • Johan Grasman, Onno A. van Herwaarden
      Pages 168-183

    6. A Markov Chain Approximation of the Stochastic Dynamical System

      • Johan Grasman, Onno A. van Herwaarden
      Pages 184-201

  5. Back Matter

    Pages 203-221
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Keywords

About this book

Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.

Authors and Affiliations

  • Department of Mathematics, Agricultural University, Wageningen, The Netherlands

    Johan Grasman, Onno A. Herwaarden

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