{
  "id": "1810.05341",
  "version": "v1",
  "published": "2018-10-12T03:33:58.000Z",
  "updated": "2018-10-12T03:33:58.000Z",
  "title": "Tails of exit times from unstable equilibria on the line",
  "authors": [
    "Yuri Bakhtin",
    "Zsolt Pajor-Gyulai"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "math.DS"
  ],
  "abstract": "For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. We give a revealing elementary proof of a result proved earlier using heavy machinery from Malliavin calculus. In particular, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically long exits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-12T03:33:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60J60",
      "37H10"
    ],
    "keywords": [
      "exit time",
      "unstable equilibrium",
      "one-dimensional smooth vector field",
      "precise vanishing noise asymptotics",
      "atypically long exits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}