Stochastic heat equations with values in a Riemannian manifold

被引:2
作者
Roeckner, Michael [1 ]
Wu, Bo [2 ,3 ]
Zhu, Rongchan [1 ,4 ]
Zhu, Xiangchan [1 ,5 ]
机构
[1] Univ Bielefeld, Dept Math, D-33615 Bielefeld, Germany
[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[3] Univ Bonn, Inst Appl Math, D-53115 Bonn, Germany
[4] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China
[5] Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China
关键词
Stochastic heat equation; Ricci curvature; functional inequality; quasi-regular Dirichlet form; SPACE; PATH;
D O I
10.4171/RLM/801
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The main result of this note is the existence of martingale solutions to the stochastic heat equation (SHE) in a Riemannian manifold by using suitable Dirichlet forms on the corresponding path/loop space. Moreover, we present some characterizations of the lower bound of the Ricci curvature by functional inequalities of various associated Dirichlet forms.
引用
收藏
页码:205 / 213
页数:9
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