The Kramers problem for SDEs driven by small, accelerated Lévy noise with exponentially light jumps
- We establish Freidlin-Wentzell results for a nonlinear ordinary differential equation starting close to the stable state 0, say, subject to a perturbation by a stochastic integral which is driven by an epsilon-small and (1/epsilon)-accelerated Levy process with exponentially light jumps. For this purpose, we derive a large deviations principle for the stochastically perturbed system using the weak convergence approach developed by Budhiraja, Dupuis, Maroulas and collaborators in recent years. In the sequel, we solve the associated asymptotic first escape problem from the bounded neighborhood of 0 in the limit as epsilon -> 0 which is also known as the Kramers problem in the literature.
| Author details: | André De Oliveira GomesGND, Michael Anton HögeleORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1142/S0219493721500192 |
| ISSN: | 0219-4937 |
| ISSN: | 1793-6799 |
| Title of parent work (English): | Stochastics and dynamics |
| Publisher: | World Scientific |
| Place of publishing: | Singapore |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/06/18 |
| Publication year: | 2021 |
| Release date: | 2024/01/02 |
| Tag: | Freidlin-Wentzell theory; accelerated small; first exit location; first passage times; large deviations principle; noise Levy diffusions; strongly tempered stable Levy measure |
| Volume: | 21 |
| Issue: | 04 |
| Article number: | 2150019 |
| Number of pages: | 44 |
| Funding institution: | project MASH [51099907]; FAPESP at UNICAMP-CampinasFundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [2018/06531-1]; School of Sciences at Universidad de los Andes; MINCIENCIAS; DFGGerman Research Foundation (DFG)European Commission |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
