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STOCHASTIC HEAT EQUATIONS FOR INFINITE STRINGS WITH VALUES IN A MANIFOLD

文献类型：期刊论文

作者Chen, Xin1; Wu, Bo2; Zhu, Rongchan3; Zhu, Xiangchan4
刊名TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
出版日期2021
卷号374期号:1页码:407-452
关键词Stochastic heat equation Ricci Curvature functional inequality quasi-regular Dirichlet form infinite volume
ISSN号0002-9947
DOI10.1090/tran/8193
英文摘要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.
资助项目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研究方向Mathematics
语种英语
WOS记录号WOS:000604947700013
出版者AMER MATHEMATICAL SOC
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58052]  
专题应用数学研究所
通讯作者Chen, Xin
作者单位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
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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