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

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 fr...

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Bibliographic Details
Main Authors: Grasman, Johan, Herwaarden, Onno A., van (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1999, 1999
Edition:1st ed. 1999
Series:Springer Series in Synergetics
Subjects:
Complex Systems
Computer Science
Mathematical Analysis
Probability Theory
Analysis
System Theory
Mathematical Physics
Theory Of Computation
Theoretical, Mathematical And Computational Physics
Mathematical Methods In Physics
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I The Fokker—Planck Equation
  • 1. Dynamical Systems Perturbed by Noise: the Langevin Equation
  • 2. The Fokker—Planck Equation: First Exit from a Domain
  • 3. The Fokker—Planck Equation: One Dimension
  • II Asymptotic Solution of the Exit Problem
  • 4. Singular Perturbation Analysis of the Differential Equations for the Exit Probability and Exit Time in One Dimension
  • 5. The Fokker—Planck Equation in Several Dimensions: the Asymptotic Exit Problem
  • III Applications
  • 6. Dispersive Groundwater Flow and Pollution
  • 7. Extinction in Systems of Interacting Biological Populations
  • 8. Stochastic Oscillation
  • 9. Confidence Domain, Return Time and Control
  • 10. A Markov Chain Approximation of the Stochastic Dynamical System
  • Literature
  • Answers to Exercises
  • Author Index

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