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

来源：

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2018年 / 29卷 / 01期

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

页码：205 / 213

页数：9

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