{
  "id": "1604.04819",
  "version": "v1",
  "published": "2016-04-17T02:35:00.000Z",
  "updated": "2016-04-17T02:35:00.000Z",
  "title": "Small Mass Limit of a Langevin Equation on a Manifold",
  "authors": [
    "Jeremiah Birrell",
    "Scott Hottovy",
    "Giovanni Volpe",
    "Jan Wehr"
  ],
  "comment": "47 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study damped geodesic motion of a particle of mass $m$ on a Riemannian manifold, in the presence of an external force and noise. Lifting the resulting stochastic differential equation to the orthogonal frame bundle, we prove that, as $m \\to 0$, its solutions converge to solutions of a limiting equation which includes a noise-induced drift term. A very special case of the main result presents the Brownian motion on the manifold as a limit of inertial systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-17T02:35:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small mass limit",
      "langevin equation",
      "resulting stochastic differential equation",
      "orthogonal frame bundle",
      "study damped geodesic motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404819B"
    }
  }
}