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Exponential asymptotics in the small parameter exit problem
Published online by Cambridge University Press: 22 January 2016
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Let M be a d-dimensional Riemannian manifold of class C∞ with Riemannian metric 
and let D be a connected domain in M having a non-empty smooth boundary 
and a compact closure 
. Suppose that 
are given and that 
converges uniformly to 
on D′ as 
for some neighborhood D′ of D. Consider the diffusion process 
on D′ with a small parameter 
generated by
(1.1) 
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- Research Article
- Information
- Copyright
- Copyright © Editorial Board of Nagoya Mathematical Journal 1996
References
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Freidlin, M. I. and Wentzell, A. D., “Random perturbations of dynamical systems,” Springer-Verlag, Berlin Heidelberg New York, 1984.Google Scholar
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Palis, J. Jr. and de Melo, W., “Geometric theory of dynamical systems, An introduction,” Springer-Verlag
New York, 1982.Google Scholar
[Sul]
Sugiura, M., Limit theorems related to the small parameter exit problems and the singularly perturbed Dirichlet problems, preprint, 1994.Google Scholar
[Su2]
Sugiura, M.
Metastable behaviors of diffusion processes with small parameter, J. Math. Soc. Japan, 47 (1995) 755–788.Google Scholar
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