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Singular Perturbation Analysis of the Differential Equations for the Exit Probability and Exit Time in One Dimension

  • Johan Grasman
  • Onno A. van Herwaarden
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

In this chapter we construct asymptotic solutions for one-dimensional exit problems directly from the differential equation using the singular perturbation method. However, in some of these problems the standard method fails and we have to introduce more refined methods such as the WKB-method or a variational approach. Of course we may as well produce an exact solution and make an asymptotic approximation with the Laplace method applied to this exact solution. We choose to carry out a singular perturbation analysis because this method can be employed in higher dimensional problems for which an exact solution is not available. The present class of one-dimensional problems offers an excellent opportunity to develop the appropriate tools and to explore the scope of the method.

Keywords

Singular Perturbation Exit Time Divergence Theorem Extinction Time Outer Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

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

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