Nonparametric Diffusivity Estimation for the Stochastic Heat Equation from Noisy Observations
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915306622943232 |
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| author | Pasemann, Gregor Reiß, Markus |
| author_facet | Pasemann, Gregor Reiß, Markus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonparametric Diffusivity Estimation for the Stochastic Heat Equation from Noisy Observations Pasemann, Gregor Reiß, Markus Statistics Theory 60H15, 62G05, 62M30 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. |
| title | Nonparametric Diffusivity Estimation for the Stochastic Heat Equation from Noisy Observations |
| topic | Statistics Theory 60H15, 62G05, 62M30 |
| url | https://arxiv.org/abs/2410.00677 |