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 |
|---|---|
| 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 |
