Path-by-path uniqueness for stochastic differential equations under Krylov-Röckner condition
- We show that any stochastic differential equation (SDE) driven by Brownian motion with drift satisfying the Krylov-Röckner condition has exactly one solution in an ordinary sense for almost every trajectory of the Brownian motion. Additionally, we show that such SDE is strongly complete, i.e. for almost every trajectory of the Brownian motion, the family of solutions with different initial data forms a continuous semiflow for all nonnegative times.
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| Author: | Lukas Anzeletti, Khoa Lê, Chengcheng LingGND |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/108662 |
| Parent Title (English): | arXiv |
| Type: | Preprint |
| Language: | English |
| Year of first Publication: | 2023 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/10/24 |
| Issue: | arXiv:2304.06802 |
| DOI: | https://doi.org/10.48550/arXiv.2304.06802 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Latest Publications (not yet published in print): | Aktuelle Publikationen (noch nicht gedruckt erschienen) |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
