Stochastic Heat Equations with Values in a Riemannian Manifold

Michael Rockner; Bo Wu; Rongchan Zhu; Xiangchan Zhu

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arXiv · 1706.05979

Stochastic Heat Equations with Values in a Riemannian Manifold

Michael Rockner·Bo Wu·Rongchan Zhu·Xiangchan Zhu

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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.

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BibTeX RIS

Michael Rockner, Bo Wu, Rongchan Zhu, Xiangchan Zhu. 2017-06-19. Stochastic Heat Equations with Values in a Riemannian Manifold. https://arxiv.org/abs/1706.05979

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