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arXiv · 2410.00677

Nonparametric Diffusivity Estimation for the Stochastic Heat Equation from Noisy Observations

Gregor Pasemann·Markus Reiß
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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.

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Gregor Pasemann, Markus Reiß. 2024-10-01. Nonparametric Diffusivity Estimation for the Stochastic Heat Equation from Noisy Observations. https://arxiv.org/abs/2410.00677

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