Michael Rockner, Bo Wu, Rongchan Zhu, Xiangchan Zhu
Published 2017-06-19Version 1
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.
Comments: short version without proof
Stochastic Heat Equations with Values in a Manifold via Dirichlet Forms
Path properties of the solution to the stochastic heat equation with Lévy noise
An $L_p$-estimate for the stochastic heat equation on an angular domain in $\mathbb{R}^2$
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