Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914789622546432 |
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| author | Dou, Fangfang Lü, Peimin Wang, Yu |
| author_facet | Dou, Fangfang Lü, Peimin Wang, Yu |
| contents | In this paper, we investigate an ill-posed Cauchy problem involving a stochastic parabolic equation. We first establish a Carleman estimate for this equation. Leveraging this estimate, we derive the conditional stability and convergence rate of the Tikhonov regularization method for the aforementioned ill-posed Cauchy problem. To complement our theoretical analysis, we employ kernel-based learning theory to implement the completed Tikhonov regularization method for several numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15741 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation Dou, Fangfang Lü, Peimin Wang, Yu Numerical Analysis 35R30, 65N21, 60H15 In this paper, we investigate an ill-posed Cauchy problem involving a stochastic parabolic equation. We first establish a Carleman estimate for this equation. Leveraging this estimate, we derive the conditional stability and convergence rate of the Tikhonov regularization method for the aforementioned ill-posed Cauchy problem. To complement our theoretical analysis, we employ kernel-based learning theory to implement the completed Tikhonov regularization method for several numerical examples. |
| title | Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation |
| topic | Numerical Analysis 35R30, 65N21, 60H15 |
| url | https://arxiv.org/abs/2308.15741 |