STOCHASTIC HEAT EQUATIONS FOR INFINITE STRINGS WITH VALUES IN A MANIFOLD

doi:10.1090/tran/8193

CSpace > 应用数学研究所

	STOCHASTIC HEAT EQUATIONS FOR INFINITE STRINGS WITH VALUES IN A MANIFOLD
	Chen, Xin 1; Wu, Bo 2; Zhu, Rongchan 3; Zhu, Xiangchan4
	2021
发表期刊	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9947
卷号	374 期号:1 页码:407-452
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.
关键词	Stochastic heat equation Ricci Curvature functional inequality quasi-regular Dirichlet form infinite volume
DOI	10.1090/tran/8193
收录类别	SCI
语种	英语
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
WOS类目	Mathematics
WOS记录号	WOS:000604947700013
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58053
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.