Nonparametric Diffusivity Estimation for the Stochastic Heat Equation from Noisy Observations

2024/10/01 by Pasemann, Gregor, Reiß, Markus
#60H15 #62G05 #62M30 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2410.00677

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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