{
  "id": "1212.5153",
  "version": "v3",
  "published": "2012-12-20T17:29:14.000Z",
  "updated": "2014-03-10T15:35:51.000Z",
  "title": "The hitting time of zero for a stable process",
  "authors": [
    "Alexey Kuznetsov",
    "Andreas E. Kyprianou",
    "Juan Carlos Pardo",
    "Alexander R. Watson"
  ],
  "journal": "Electron. J. Probab. 19 (2014), no. 30, 1-26",
  "doi": "10.1214/EJP.v19-2647",
  "categories": [
    "math.PR"
  ],
  "abstract": "For any two-sided jumping $\\alpha$-stable process, where $1 < \\alpha < 2$, we find an explicit identity for the law of the first hitting time of the origin. This complements existing work in the symmetric case and the spectrally one-sided case; cf. Yano-Yano-Yor (2009) and Cordero (2010), and Peskir (2008) respectively. We appeal to the Lamperti-Kiu representation of Chaumont-Pant\\'i-Rivero (2011) for real-valued self-similar Markov processes. Our main result follows by considering a vector-valued functional equation for the Mellin transform of the integrated exponential Markov additive process in the Lamperti-Kiu representation. We conclude our presentation with some applications.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-10T15:35:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G52",
      "60G18",
      "60G51"
    ],
    "keywords": [
      "stable process",
      "hitting time",
      "lamperti-kiu representation",
      "integrated exponential markov additive process",
      "real-valued self-similar markov processes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5153K"
    }
  }
}