Localization and metastability
- In this chapter, equipped with our previously obtained knowledge of exit and transition times in the limit of small noise amplitude ??0 , we shall investigate the global asymptotic behavior of our jump diffusion process in the time scale in which transitions occur, i.e. in the scale given by ?0(?)=?(1?Bc?(0)),?,?>0 . It turns out that in this time scale, the switching of the diffusion between neighborhoods of the stable solutions ? ± can be well described by a Markov chain jumping back and forth between two states with a characteristic Q-matrix determined by the quantities ?((D±0)c)?(Bc?(0)) as jumping rates.
Author details: | Arnaud Debussche, Michael HögeleGND, Peter Imkeller |
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DOI: | https://doi.org/10.1007/978-3-319-00828-8_7 |
ISBN: | 978-3-319-00828-8; 978-3-319-00827-1 |
ISSN: | 0075-8434 |
Title of parent work (English): | Lecture notes in mathematics : a collection of informal reports and seminars |
Title of parent work (English): | Lecture Notes in Mathematics |
Publisher: | Springer |
Place of publishing: | Berlin |
Publication type: | Article |
Language: | English |
Year of first publication: | 2013 |
Publication year: | 2013 |
Release date: | 2017/03/26 |
Volume: | 2085 |
Number of pages: | 19 |
First page: | 131 |
Last Page: | 149 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |