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oai:u-ryukyu.repo.nii.ac.jp:02005324
2022-10-31T02:38:18Z
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Asymptotic behaviors on the small parameter exit problems and the singularly perturbation problems
Sugiura, Makoto
杉浦, 誠
open access
We consider the small parameter exit problems for diffusion processes and the associated singular perturbed Dirichlet problems. We investigate the asymptotic relations between the mean exit time and the principal eigenvalue. Two problems are considered under the gradient condition for the corresponding dynamical system. One is under the uniqueness of deepest valley, where we show that the product of the mean exit time and the principal eigenvalue converges to one exponentially fast. The other is related to the sharp asymptotics of the mean exit times, the eigenvalues and eigenfunctions, where we characterize the scaling limits of them by the Markov chain which appears metastable behavior of the corresponding diffusion process. To do this, we extend the methods used in our previous papers [10] and [11].
紀要論文
Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus
2001-12-30
eng
departmental bulletin paper
VoR
http://hdl.handle.net/20.500.12000/15071
http://hdl.handle.net/20.500.12000/15071
https://u-ryukyu.repo.nii.ac.jp/records/2005324
1344-008X
AA10779580
Ryukyu mathematical journal
14
79
118
https://u-ryukyu.repo.nii.ac.jp/record/2005324/files/Vol14p079.pdf