{
  "id": "0712.2637",
  "version": "v3",
  "published": "2007-12-17T06:26:47.000Z",
  "updated": "2012-08-17T16:23:09.000Z",
  "title": "On the Limit Law of a Random Walk Conditioned to Reach a High Level",
  "authors": [
    "Sergey G. Foss",
    "Anatolii A. Puhalskii"
  ],
  "journal": "Stochastic Processes and Their Applications, 1221 (2011), 288-313",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a random walk with a negative drift and with a jump distribution which under Cram\\'er's change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally-positive L\\'evy %-Khinchin process conditioned not to overshoot level one.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-08-17T16:23:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60G51",
      "60F17"
    ],
    "keywords": [
      "high level",
      "limit law",
      "random walk converges",
      "nondecreasing markov process"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.2637F"
    }
  }
}