{
  "id": "1306.0218",
  "version": "v2",
  "published": "2013-06-02T15:17:57.000Z",
  "updated": "2015-04-26T17:29:24.000Z",
  "title": "The Martingale Property in the Context of Stochastic Differential Equations",
  "authors": [
    "Johannes Ruf"
  ],
  "comment": "Revised version. Published in Electron. Commun. Probab",
  "journal": "Electron. Commun. Probab. 20 (2015), no. 34, 1-10",
  "doi": "10.1214/ECP.v20-3449",
  "categories": [
    "math.PR"
  ],
  "abstract": "This note studies the martingale property of a nonnegative, continuous local martingale Z, given as a nonanticipative functional of a solution to a stochastic differential equation. The condition states that Z is a (uniformly integrable) martingale if and only if an integral test of a related functional holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-02T15:17:57.000Z",
      "abstract": "This note proves the existence of a solution to a certain martingale problem and relates the martingale property of a given nonnegative local martingale under one measure to an integral test of a related functional under another measure.",
      "comment": "9 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-26T17:29:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic differential equations",
      "martingale property",
      "integral test",
      "martingale problem",
      "nonnegative local martingale"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.0218R"
    }
  }
}