Agmon-type estimates for a class of jump processes
- In the limit 0 we analyse the generators H of families of reversible jump processes in Rd associated with a class of symmetric non-local Dirichlet-forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of a certain eikonal equation. Fine results are sensitive to the rate function being C2 or just Lipschitz. Our estimates are analogous to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice Zd. Although our final interest is in the (sub)stochastic jump process, technically this is a pure analysis paper, inspired by PDE techniques.
| Author details: | Markus KleinGND, Christian Leonard, Elke RosenbergerORCiD |
|---|---|
| DOI: | https://doi.org/10.1002/mana.201200324 |
| ISSN: | 0025-584X |
| ISSN: | 1522-2616 |
| Title of parent work (English): | Mathematische Nachrichten |
| Publisher: | Wiley-VCH |
| Place of publishing: | Weinheim |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2014 |
| Publication year: | 2014 |
| Release date: | 2017/03/27 |
| Tag: | Decay of eigenfunctions; Dirichlet-form; Finsler distance; jump process; semiclassical Agmon estimate |
| Volume: | 287 |
| Issue: | 17-18 |
| Number of pages: | 19 |
| First page: | 2021 |
| Last Page: | 2039 |
| Funding institution: | Deutsch-Franzosische Hochschule [DFDK-01-06] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
