KMS Of Academy of mathematics and systems sciences, CAS
| STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS | |
Roeckner, Michael1; Wu, Bo2; Zhu, Rongchan1,3; Zhu, Xiangchan1,4
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| 2020 | |
| Source Publication | SIAM JOURNAL ON MATHEMATICAL ANALYSIS
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| ISSN | 0036-1410 |
| Volume | 52Issue:3Pages:2237-2274 |
| Abstract | In this paper, we prove the existence of martingale solutions to the stochastic heat equation taking values in a Riemannian manifold, which admits the Wiener (Brownian bridge) measure on the Riemannian path (loop) space as an invariant measure using a suitable Dirichlet form. Using the Andersson-Driver approximation, we heuristically derive a form of the equation solved by the process given by the Dirichlet form. Moreover, we establish the log-Sobolev inequality for the Dirichlet form in the path space. In addition, some characterizations for the lower bound of the Ricci curvature are presented related to the stochastic heat equation. |
| Keyword | stochastic heat equation Ricci curvature functional inequality quasi-regular Dirichlet form |
| DOI | 10.1137/18M1211076 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | NSFC[11671035] ; NSFC[11771037] ; NSFC[11871338] ; NSFC[11922103] ; DFG[CRC 1283] ; Key Lab of Random Complex Structures and Data Science, Chinese Academy of Sciences |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000546975100002 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51790 |
| Collection | 应用数学研究所 |
| Corresponding Author | Zhu, Rongchan |
| Affiliation | 1.Univ Bielefeld, Dept Math, D-33615 Bielefeld, Germany 2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 3.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Roeckner, Michael,Wu, Bo,Zhu, Rongchan,et al. STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2020,52(3):2237-2274. |
| APA | Roeckner, Michael,Wu, Bo,Zhu, Rongchan,&Zhu, Xiangchan.(2020).STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,52(3),2237-2274. |
| MLA | Roeckner, Michael,et al."STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 52.3(2020):2237-2274. |
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