Non-parametric estimation of non-linear diffusion coefficient in parabolic SPDEs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911157614280704 |
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| author | Andersson, Martin Avelin, Benny Garino, Valentin Ilmonen, Pauliina Viitasaari, Lauri |
| author_facet | Andersson, Martin Avelin, Benny Garino, Valentin Ilmonen, Pauliina Viitasaari, Lauri |
| contents | In this article, we introduce a novel non-parametric predictor, based on conditional expectation, for the unknown diffusion coefficient function $σ$ in the stochastic partial differential equation $Lu = σ(u)\dot{W}$, where $L$ is a parabolic second order differential operator and $\dot{W}$ is a suitable Gaussian noise. We prove consistency and derive an upper bound for the error in the $L^p$ norm, in terms of discretization and smoothening parameters $h$ and $\varepsilon$. We illustrate the applicability of the approach and the role of the parameters with several interesting numerical examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_12921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-parametric estimation of non-linear diffusion coefficient in parabolic SPDEs Andersson, Martin Avelin, Benny Garino, Valentin Ilmonen, Pauliina Viitasaari, Lauri Statistics Theory 62G05 (Primary), 60H15 (Secondary) In this article, we introduce a novel non-parametric predictor, based on conditional expectation, for the unknown diffusion coefficient function $σ$ in the stochastic partial differential equation $Lu = σ(u)\dot{W}$, where $L$ is a parabolic second order differential operator and $\dot{W}$ is a suitable Gaussian noise. We prove consistency and derive an upper bound for the error in the $L^p$ norm, in terms of discretization and smoothening parameters $h$ and $\varepsilon$. We illustrate the applicability of the approach and the role of the parameters with several interesting numerical examples. |
| title | Non-parametric estimation of non-linear diffusion coefficient in parabolic SPDEs |
| topic | Statistics Theory 62G05 (Primary), 60H15 (Secondary) |
| url | https://arxiv.org/abs/2509.12921 |