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 STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS Roeckner, Michael1; Wu, Bo2; Zhu, Rongchan1,3; Zhu, Xiangchan1,4 2020 Source Publication SIAM JOURNAL ON MATHEMATICAL ANALYSIS ISSN 0036-1410 Volume 52Issue:3Pages:2237-2274 Abstract 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. Keyword stochastic heat equation Ricci curvature functional inequality quasi-regular Dirichlet form DOI 10.1137/18M1211076 Indexed By SCI Language 英语 Funding Project 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 Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000546975100002 Publisher SIAM PUBLICATIONS Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/51790 Collection 应用数学研究所 Corresponding Author Zhu, Rongchan Affiliation 1.Univ Bielefeld, Dept Math, D-33615 Bielefeld, Germany2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China3.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China Recommended CitationGB/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.
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