{
  "id": "1103.4251",
  "version": "v1",
  "published": "2011-03-22T12:12:28.000Z",
  "updated": "2011-03-22T12:12:28.000Z",
  "title": "On exit time of stable processes",
  "authors": [
    "Piotr Graczyk",
    "Tomasz Jakubowski"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the exit time $\\tau=\\tau_{(0,\\infty)}$ for 1-dimensional strictly stable processes and express its Laplace transform at $t^\\alpha$ as the Laplace transform of a positive random variable with explicit density. Consequently, $\\tau$ satisfies some multiplicative convolution relations. For some stable processes, e.g. for the symmetric $\\frac23$-stable process, explicit formulas for the Laplace transform and the density of $\\tau$ are obtained as an application.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-22T12:12:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G52"
    ],
    "keywords": [
      "exit time",
      "laplace transform",
      "explicit formulas",
      "explicit density",
      "multiplicative convolution relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.4251G"
    }
  }
}