{
  "id": "math/0505515",
  "version": "v2",
  "published": "2005-05-24T20:29:20.000Z",
  "updated": "2007-08-03T22:21:51.000Z",
  "title": "A class of remarkable submartingales",
  "authors": [
    "Ashkan Nikeghbali"
  ],
  "comment": "Typos corrected. Close to the published version",
  "journal": "Stochastic Processes and their applications; 116 - p.917-938 (2006)",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we consider the special class of positive local submartingales (X_{t}) of the form: X_{t}=N_{t}+A_{t}, where the measure (dA_{t}) is carried by the set {t: X_{t}=0}. We show that many examples of stochastic processes studied in the literature are in this class and propose a unified approach based on martingale techniques to study them. In particular, we establish some martingale characterizations for these processes and compute explicitly some distributions involving the pair (X_{t},A_{t}). We also associate with X a solution to the Skorokhod's stopping problem for probability measures on the positive half-line.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-03T22:21:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38",
      "15A15",
      "15A18"
    ],
    "keywords": [
      "positive local submartingales",
      "stochastic processes",
      "special class",
      "probability measures",
      "martingale techniques"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5515N"
    }
  }
}