{
  "id": "0712.3468",
  "version": "v1",
  "published": "2007-12-20T15:42:03.000Z",
  "updated": "2007-12-20T15:42:03.000Z",
  "title": "Martingales and first passage times of AR(1) sequences",
  "authors": [
    "Alexander Novikov",
    "Nino Kordzakhia"
  ],
  "comment": "To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (http://imstat.org/publications/lecnotes.htm)",
  "categories": [
    "math.PR"
  ],
  "abstract": "Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences (AR(1)). Further, we prove a martingale identity to be used in obtaining explicit bounds for the expectation of first passage times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-20T15:42:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A30",
      "60J55",
      "49J15"
    ],
    "keywords": [
      "first passage times",
      "ergodic first order autoregressive sequences",
      "martingale approach",
      "obtaining explicit bounds",
      "sufficient conditions"
    ],
    "tags": [
      "monograph",
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3468N"
    }
  }
}