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STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS

文献类型：期刊论文

作者Roeckner, Michael1; Wu, Bo2; Zhu, Rongchan1,3; Zhu, Xiangchan1,4
刊名SIAM JOURNAL ON MATHEMATICAL ANALYSIS
出版日期2020
卷号52期号:3页码:2237-2274
关键词stochastic heat equation Ricci curvature functional inequality quasi-regular Dirichlet form
ISSN号0036-1410
DOI10.1137/18M1211076
英文摘要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.
资助项目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研究方向Mathematics
语种英语
WOS记录号WOS:000546975100002
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/51789]  
专题应用数学研究所
通讯作者Zhu, Rongchan
作者单位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
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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