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Nonparametric Diffusivity Estimation for the Stochastic H...
[Submitted on 1 Oct 2024 (v1), last revised 3 Jul 2026 (this ver · 2024-10-01 · via math.ST updates on arXiv.org

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Abstract:We estimate nonparametrically the spatially varying diffusivity of a stochastic heat equation from observations perturbed by additional noise. To that end, we employ a two-step localization procedure, more precisely, we combine local state estimates into a locally linear regression approach. Our analysis relies on quantitative Trotter--Kato type approximation results for the heat semigroup that are of independent interest. The presence of observational noise leads to non-standard scaling behaviour of the model. Numerical simulations illustrate the results.

Submission history

From: Gregor Pasemann [view email]
[v1] Tue, 1 Oct 2024 13:35:07 UTC (415 KB)
[v2] Tue, 27 May 2025 11:04:35 UTC (415 KB)
[v3] Fri, 3 Jul 2026 10:27:53 UTC (417 KB)