@article{fd1a881dd4b8447fa31b9e0f4a8e8e16,
title = "Stochastic heat equations with values in a Riemannian manifold",
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.",
keywords = "Functional inequality, Quasi-regular Dirichlet form, Ricci curvature, Stochastic heat equation",
author = "Michael R{\"o}ckner and Bo Wu and Rongchan Zhu and Xiangchan Zhu",
note = "Publisher Copyright: {\textcopyright} 2018 European Mathematical Society Publishing House. All rights reserved.",
year = "2018",
doi = "10.4171/RLM/801",
language = "English",
volume = "29",
pages = "205--213",
journal = "Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni",
issn = "1120-6330",
publisher = "European Mathematical Society Publishing House",
number = "1",
}