On MAP estimates and source conditions for drift identification in SDEs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917407669354496 |
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| author | Tenbrinck, Daniel Uesseler, Nikolas Wacker, Philipp Wirth, Benedikt |
| author_facet | Tenbrinck, Daniel Uesseler, Nikolas Wacker, Philipp Wirth, Benedikt |
| contents | We consider the inverse problem of identifying the drift in an SDE from $n$ observations of its solution at $M+1$ distinct time points. We derive a corresponding MAP estimate, we prove differentiability properties as well as a so-called tangential cone condition for the forward operator, and we review the existing theory for related problems, which under a slightly stronger tangential cone condition would additionally yield convergence rates for the MAP estimate as $n\to\infty$. Numerical simulations in 1D indicate that such convergence rates indeed hold true. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18443 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On MAP estimates and source conditions for drift identification in SDEs Tenbrinck, Daniel Uesseler, Nikolas Wacker, Philipp Wirth, Benedikt Numerical Analysis We consider the inverse problem of identifying the drift in an SDE from $n$ observations of its solution at $M+1$ distinct time points. We derive a corresponding MAP estimate, we prove differentiability properties as well as a so-called tangential cone condition for the forward operator, and we review the existing theory for related problems, which under a slightly stronger tangential cone condition would additionally yield convergence rates for the MAP estimate as $n\to\infty$. Numerical simulations in 1D indicate that such convergence rates indeed hold true. |
| title | On MAP estimates and source conditions for drift identification in SDEs |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.18443 |