JournalsrlmVol. 29, No. 1pp. 205–213

Stochastic heat equations with values in a Riemannian manifold

  • Michael Röckner

    Universität Bielefeld, Germany

  • Bo Wu

    Fudan University, Shanghai, China and University of Bonn, Germany

  • Rongchan Zhu

    Bejing Institute of Technology, China and University of Bielefeld, Germany

  • Xiangchan Zhu

    Bejing Jiaotong University, China and University of Bielefeld, Germany
Stochastic heat equations with values in a Riemannian manifold cover
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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.

Cite this article

Michael Röckner, Bo Wu, Rongchan Zhu, Xiangchan Zhu, Stochastic heat equations with values in a Riemannian manifold. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 1, pp. 205–213

DOI 10.4171/RLM/801