STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS

doi:10.1137/18M1211076

CSpace > 应用数学研究所

	STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS
	Roeckner, Michael 1; Wu, Bo 2; Zhu, Rongchan 1,3; Zhu, Xiangchan1,4
	2020
发表期刊	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN	0036-1410
卷号	52 期号:3 页码:2237-2274
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.
关键词	stochastic heat equation Ricci curvature functional inequality quasi-regular Dirichlet form
DOI	10.1137/18M1211076
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000546975100002
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51790
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.