{
  "id": "1811.00827",
  "version": "v1",
  "published": "2018-11-02T11:36:23.000Z",
  "updated": "2018-11-02T11:36:23.000Z",
  "title": "Time since maximum of Brownian motion and asymmetric Levy processes",
  "authors": [
    "Richard J. Martin",
    "Michael J. Kearney"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Motivated by recent studies of record statistics in relation to strongly correlated time series, we consider explicitly the drawdown time of a Levy process, which is defined as the time since it last achieved its running maximum when observed over a fixed time period [0,T]. We show that the density function of this drawdown time, in the case of a completely asymmetric jump process, may be factored as a function of $t$ multiplied by a function of T-t. This extends a known result for the case of pure Brownian motion. We state the factors explicitly for the cases of exponential down-jumps with drift, and for the downward Inverse Gaussian Levy process with drift.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-02T11:36:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymmetric levy processes",
      "drawdown time",
      "downward inverse gaussian levy process",
      "pure brownian motion",
      "asymmetric jump process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}