{
  "id": "1706.05979",
  "version": "v1",
  "published": "2017-06-19T14:15:52.000Z",
  "updated": "2017-06-19T14:15:52.000Z",
  "title": "Stochastic Heat Equations with Values in a Riemannian Manifold",
  "authors": [
    "Michael Rockner",
    "Bo Wu",
    "Rongchan Zhu",
    "Xiangchan Zhu"
  ],
  "comment": "short version without proof",
  "categories": [
    "math.PR",
    "math.AP",
    "math.DG",
    "math.FA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-19T14:15:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic heat equation",
      "riemannian manifold",
      "corresponding path/loop space",
      "martingale solutions",
      "associated dirichlet forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}