Markovianity and ergodicity for a surface growth PDE
- The paper analyses a model in surface growth, where uniqueness of weak solutions seems to be out of reach. We provide the existence of a weak martingale solution satisfying energy inequalities and having the Markov property. Furthermore, under non-degeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure.
| Author: | Dirk BlömkerORCiDGND, Franco Flandoli, Marco RomitoORCiD |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-4514 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/558 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2007-30) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2007/07/13 |
| Year of first Publication: | 2007 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2007/07/13 |
| Tag: | Markov solutions; Surface growth model; ergodicity; strong Feller property; weak energy solutions |
| GND-Keyword: | Partielle Differentialgleichung; Markov-Prozess; Feller-Prozess; Schwache Lösung; Wachstumsmodell; Ergodentheorie |
| Note: | Erschienen in The Annals of Probability, 37, 1, S. 275-313, https://doi.org/10.1214/08-aop403 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
