Small dispersion asymptotics for an SPDE in two space dimensions using triple increments
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911977169747968 |
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| author | Tonaki, Yozo Kaino, Yusuke Uchida, Masayuki |
| author_facet | Tonaki, Yozo Kaino, Yusuke Uchida, Masayuki |
| contents | We consider parametric estimation for a second order linear parabolic stochastic partial differential equation (SPDE) in two space dimensions driven by a $Q$-Wiener process with a small noise based on high frequency spatio-temporal data. We first provide estimators of the diffusive and advective parameters in the SPDE using temporal and spatial increments. We then construct an estimator of the reaction parameter in the SPDE based on an approximate coordinate process. We also give simulation results of the proposed estimators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small dispersion asymptotics for an SPDE in two space dimensions using triple increments Tonaki, Yozo Kaino, Yusuke Uchida, Masayuki Statistics Theory We consider parametric estimation for a second order linear parabolic stochastic partial differential equation (SPDE) in two space dimensions driven by a $Q$-Wiener process with a small noise based on high frequency spatio-temporal data. We first provide estimators of the diffusive and advective parameters in the SPDE using temporal and spatial increments. We then construct an estimator of the reaction parameter in the SPDE based on an approximate coordinate process. We also give simulation results of the proposed estimators. |
| title | Small dispersion asymptotics for an SPDE in two space dimensions using triple increments |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2408.02224 |