Work

Nonparametric Diffusivity Estimation for the Stochastic Heat Equation from Noisy Observations

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2410.00677

Authors: Pasemann, Gregor, Reiß, Markus

Institution: Humboldt-Universität zu Berlin

Language: English

Topic: Control Systems and Identification

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: G2601165318, SFB 1294: Datenassimilation – Die nahtlose Verschmelzung von Daten und Modellen

OpenAlex ID: W4403820950

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