Stochastic heat equations with values in a Riemannian manifold

Michael Röckner; Bo Wu; Rongchan Zhu; Xiangchan Zhu

doi:10.4171/RLM/801

Stochastic heat equations with values in a Riemannian manifold

Michael Röckner, Bo Wu, Rongchan Zhu, Xiangchan Zhu

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	205-213
Number of pages	9
Journal	Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
Volume	29
Issue number	1
DOIs	https://doi.org/10.4171/RLM/801
Publication status	Published - 2018

Keywords

Functional inequality
Quasi-regular Dirichlet form
Ricci curvature
Stochastic heat equation

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10.4171/RLM/801

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Röckner, M., Wu, B., Zhu, R., & Zhu, X. (2018). Stochastic heat equations with values in a Riemannian manifold. Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni, 29(1), 205-213. https://doi.org/10.4171/RLM/801

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AU - Wu, Bo

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AU - Zhu, Xiangchan

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KW - Functional inequality

KW - Quasi-regular Dirichlet form

KW - Ricci curvature

KW - Stochastic heat equation

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Stochastic heat equations with values in a Riemannian manifold

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Keywords

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