The Weak-Noise Characteristic Boundary Exit Problem: Old and New Results

  • R. S. Maier
  • D. L. Stein
Part of the Institute for Nonlinear Science book series (INLS)


The problem of noise-induced escape from a metastable state arises in many areas of science. If the dynamics of the system under investigation are specified by a nongradient drift field, many classical results on the weak-noise limit do not apply. The absence of gradient deterministic dynamics can lead to rarely considered, nonintuitive phenomena, such as most probable exit paths from a domain of attraction that terminate at unstable fixed points (mountain peaks) rather than the usual saddle points; non-Gaussian limiting distributions of exit points; and the appearance of focusing singularities along the most probable exit paths. We discuss these novel phenomena.


Saddle Point Unstable Manifold Detailed Balance Stable Fixed Point Mountain Peak 
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© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • R. S. Maier
  • D. L. Stein

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