The Milstein scheme for singular SDEs with Hölder continuous drift
- We study the Lp rate of convergence of the Milstein scheme for SDEs when the drift coefficients possess only Hölder regularity. If the diffusion is elliptic and sufficiently regular, we obtain rates consistent with the additive case. The proof relies on regularisation by noise techniques, particularly stochastic sewing, which in turn requires (at least asymptotically) sharp estimates on the law of the Milstein scheme, which may be of independent interest.
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| Author: | Máté Gerencsér, Gerald Lampl, Chengcheng LingGND |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/108611 |
| Parent Title (English): | arXiv |
| Type: | Preprint |
| Language: | English |
| Year of first Publication: | 2023 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/10/24 |
| Issue: | arXiv:2305.16004 |
| DOI: | https://doi.org/10.48550/arXiv.2305.16004 |
| 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) |
