{
  "id": "2004.00358",
  "version": "v1",
  "published": "2020-04-01T12:06:38.000Z",
  "updated": "2020-04-01T12:06:38.000Z",
  "title": "Large deviations for Brownian motion in evolving Riemannian manifolds",
  "authors": [
    "Rik Versendaal"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove large deviations for $g(t)$-Brownian motion in a complete, evolving Riemannian manifold $M$ with respect to a collection $\\{g(t)\\}_{t\\in [0,1]}$ of Riemannian metrics, smoothly depending on $t$. We show how the large deviations are obtained from the large deviations of the (time-dependent) horizontal lift of $g(t)$-Brownian motion to the frame bundle $FM$ over $M$. The latter is proved by embedding the frame bundle into some Euclidean space and applying Freidlin-Wentzell theory for diffusions with time-dependent coefficients, where the coefficients are jointly Lipschitz in space and time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-01T12:06:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "58J65"
    ],
    "keywords": [
      "large deviations",
      "evolving riemannian manifold",
      "brownian motion",
      "frame bundle",
      "time-dependent coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}