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arXiv · 2507.18443

On MAP estimates and source conditions for drift identification in SDEs

Daniel Tenbrinck·Nikolas Uesseler·Philipp Wacker·Benedikt Wirth
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Abstract

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.

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Daniel Tenbrinck, Nikolas Uesseler, Philipp Wacker, Benedikt Wirth. 2025-07-24. On MAP estimates and source conditions for drift identification in SDEs. https://arxiv.org/abs/2507.18443

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