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Exponential asymptotics in the small parameter exit problem

Published online by Cambridge University Press:  22 January 2016

Makoto Sugiura
Makoto Sugiura*
Affiliation:
Graduate School of Polymathematics, Nagoya University, Nagoya 464-01, Japan, email: sugiura@math.nagoya-u.ac.jp
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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)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 144 , December 1996 , pp. 137 - 154
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

[FW] Freidlin, M. I. and Wentzell, A. D., “Random perturbations of dynamical systems,” Springer-Verlag, Berlin Heidelberg New York, 1984.Google Scholar
[PD] 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