STOCHASTIC HEAT EQUATIONS FOR INFINITE STRINGS WITH VALUES IN A MANIFOLD

doi:10.1090/tran/8193

	STOCHASTIC HEAT EQUATIONS FOR INFINITE STRINGS WITH VALUES IN A MANIFOLD
	Chen, Xin 2; Wu, Bo 3; Zhu, Rongchan 1; Zhu, Xiangchan 4
刊名	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
	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
DOI	10.1090/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
出版者	AMER MATHEMATICAL SOC
WOS记录号	WOS:000604947700013
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58052]
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Xin
作者单位	1.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 2.Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China 3.Fudan Univ, Sch Math Sci, Shanghai 200433, 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.