{
  "id": "0811.1696",
  "version": "v2",
  "published": "2008-11-11T12:49:26.000Z",
  "updated": "2008-12-18T14:30:45.000Z",
  "title": "Measure changes with extinction",
  "authors": [
    "Simon Harris",
    "Matthew Roberts"
  ],
  "comment": "6 pages; corrected typo, shortened proof of Theorem 6",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a change of measure by a martingale $Z_t$ and clarify that in general $1/Z_t$ is only a supermartingale under the changed measure. We then give a necessary and sufficient condition for the event that the limit of the martingale is zero to coincide with the event that the martingale hits zero in finite time (up to a set of zero probability).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-18T14:30:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G99"
    ],
    "keywords": [
      "measure changes",
      "extinction",
      "martingale hits zero",
      "sufficient condition",
      "finite time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.1696H"
    }
  }
}