Nonparametric Diffusivity Estimation for the Stochastic Heat Equation from Noisy Observations
Statistics Theory
2025-05-28 v2 Statistics Theory
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.
Cite
@article{arxiv.2410.00677,
title = {Nonparametric Diffusivity Estimation for the Stochastic Heat Equation from Noisy Observations},
author = {Gregor Pasemann and Markus Reiß},
journal= {arXiv preprint arXiv:2410.00677},
year = {2025}
}