KMS Of Academy of mathematics and systems sciences, CAS
| STOCHASTIC HEAT EQUATIONS FOR INFINITE STRINGS WITH VALUES IN A MANIFOLD | |
Chen, Xin1; Wu, Bo2; Zhu, Rongchan3; Zhu, Xiangchan4
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| 2021 | |
| Source Publication | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
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| ISSN | 0002-9947 |
| Volume | 374Issue:1Pages:407-452 |
| Abstract | In the paper, we construct conservative Markov processes corresponding to the martingale solutions to the stochastic heat equation on R+ or R with values in a general Riemannian manifold, which is only assumed to be complete and stochastic complete. This work is an extension of the previous paper of Rockner and the second, third, and fourth authors [SIAM J. Math. Anal. 52 (2020), pp. 2237-2274] on finite volume case. Moveover, we also obtain some functional inequalities associated to these Markov processes. This implies that on infinite volume case, the exponential ergodicity of the solution of the Ricci curvature is strictly positive and the non-ergodicity of the process if the sectional curvature is negative. |
| Keyword | Stochastic heat equation Ricci Curvature functional inequality quasi-regular Dirichlet form infinite volume |
| DOI | 10.1090/tran/8193 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | NSFC[11671035] ; NSFC[11771037] ; NSFC[11922103] ; NSFC[12071085] ; NSFC[11871338] ; DFG[CRC 1283] ; key Lab of Random Complex Structures and Data Science, Chinese Academy of Science |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000604947700013 |
| Publisher | AMER MATHEMATICAL SOC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58053 |
| Collection | 应用数学研究所 |
| Corresponding Author | Chen, Xin |
| Affiliation | 1.Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China 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 | Chen, Xin,Wu, Bo,Zhu, Rongchan,et al. STOCHASTIC HEAT EQUATIONS FOR INFINITE STRINGS WITH VALUES IN A MANIFOLD[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2021,374(1):407-452. |
| APA | Chen, Xin,Wu, Bo,Zhu, Rongchan,&Zhu, Xiangchan.(2021).STOCHASTIC HEAT EQUATIONS FOR INFINITE STRINGS WITH VALUES IN A MANIFOLD.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,374(1),407-452. |
| MLA | Chen, Xin,et al."STOCHASTIC HEAT EQUATIONS FOR INFINITE STRINGS WITH VALUES IN A MANIFOLD".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 374.1(2021):407-452. |
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