{
  "id": "1106.5389",
  "version": "v1",
  "published": "2011-06-27T13:36:40.000Z",
  "updated": "2011-06-27T13:36:40.000Z",
  "title": "Stability of the Exit Time for Lévy Processes",
  "authors": [
    "Philip S. Griffin",
    "Ross A. Maller"
  ],
  "journal": "Adv. Appl. Probab. 43, 712-734 (2011)",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper is concerned with the behaviour of a L\\'{e}vy process when it crosses over a positive level, $u$, starting from 0, both as $u$ becomes large and as $u$ becomes small. Our main focus is on the time, $\\tau_u$, it takes the process to transit above the level, and in particular, on the {\\it stability} of this passage time; thus, essentially, whether or not $\\tau_u$ behaves linearly as $u\\dto 0$ or $u\\to\\infty$. We also consider conditional stability of $\\tau_u$ when the process drifts to $-\\infty$, a.s. This provides information relevant to quantities associated with the ruin of an insurance risk process, which we analyse under a Cram\\'er condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-27T13:36:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60K05",
      "91B30"
    ],
    "keywords": [
      "exit time",
      "lévy processes",
      "insurance risk process",
      "passage time",
      "cramer condition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.5389G"
    }
  }
}