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

  • Johan Grasman
  • Onno A. van Herwaarden

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

Table of contents

  1. Front Matter
    Pages I-IX
  2. The Fokker—Planck Equation

    1. Front Matter
      Pages 1-1
    2. Johan Grasman, Onno A. van Herwaarden
      Pages 3-17
    3. Johan Grasman, Onno A. van Herwaarden
      Pages 18-26
    4. Johan Grasman, Onno A. van Herwaarden
      Pages 27-39
  3. Asymptotic Solution of the Exit Problem

  4. Applications

    1. Front Matter
      Pages 97-97
    2. Johan Grasman, Onno A. van Herwaarden
      Pages 99-117
    3. Johan Grasman, Onno A. van Herwaarden
      Pages 118-148
    4. Johan Grasman, Onno A. van Herwaarden
      Pages 149-167
    5. Johan Grasman, Onno A. van Herwaarden
      Pages 168-183
    6. Johan Grasman, Onno A. van Herwaarden
      Pages 184-201
  5. Back Matter
    Pages 203-221

About this book

Introduction

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 where 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.

Keywords

Approximation Boundary value problem Fokker-Planck equation Markov Markov chain calculus differential equation dynamical systems dynamische Systeme

Authors and affiliations

  • Johan Grasman
    • 1
  • Onno A. van Herwaarden
    • 1
  1. 1.Department of MathematicsAgricultural UniversityWageningenThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03857-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08409-6
  • Online ISBN 978-3-662-03857-4
  • Series Print ISSN 0172-7389
  • Buy this book on publisher's site
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