{
  "id": "1307.4482",
  "version": "v2",
  "published": "2013-07-17T01:48:23.000Z",
  "updated": "2013-07-27T05:03:16.000Z",
  "title": "Functional inequalities on path space over a non-compact Riemannian manifold",
  "authors": [
    "Xin Chen",
    "Bo Wu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove the existence of the O-U Dirichlet form and the damped O-U Dirichlet form on path space over a general non-compact Riemannian manifold which is complete and stochastically complete. We show a weighted log-Sobolev inequality for the O-U Dirichlet form and the (standard) log-Sobolev inequality for the damped O-U Dirichlet form. In particular, the Poincar\\'e inequality (and the super Poincar\\'e inequality) can be established for the O-U Dirichlet form on path space over a class of Riemannian manifolds with unbounded Ricci curvatures. Moreover, we construct a large class of quasi-regular local Dirichlet forms with unbounded random diffusion coefficients on the path space over a general non-compact manifold.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-27T05:03:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J65"
    ],
    "keywords": [
      "path space",
      "functional inequalities",
      "damped o-u dirichlet form",
      "quasi-regular local dirichlet forms",
      "poincare inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.4482C"
    }
  }
}