{
  "id": "1809.00560",
  "version": "v1",
  "published": "2018-09-03T11:39:31.000Z",
  "updated": "2018-09-03T11:39:31.000Z",
  "title": "Excursions of a spectrally negative Lévy process from a two-point set",
  "authors": [
    "Matija Vidmar"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $a\\in (0,\\infty)$. For a spectrally negative L\\'evy process $X$ with infinite variation paths the resolvent of the process killed on hitting the two-point set $V=\\{-a,a\\}$ is identified. When further $X$ has no diffusion component the Laplace transforms of the entrance laws of the excursion measures of $X$ from $V$ are determined. This is then applied to establishing the Laplace transform of the amount of time that elapses between the last visit of $X$ to a given point $x$, before hitting some other point $y>x$, and the hitting time of $y$. All the expressions are explicit and tractable in the standard fluctuation quantities associated to $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-03T11:39:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60J25"
    ],
    "keywords": [
      "spectrally negative lévy process",
      "two-point set",
      "laplace transform",
      "standard fluctuation quantities",
      "infinite variation paths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}