{
  "id": "1807.00486",
  "version": "v1",
  "published": "2018-07-02T06:39:41.000Z",
  "updated": "2018-07-02T06:39:41.000Z",
  "title": "Exit problems for positive self-similar Markov processes with one-sided jumps",
  "authors": [
    "Matija Vidmar"
  ],
  "comment": "19 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "A systematic exposition of scale functions is given for positive self-similar Markov processes (pssMp) with one-sided jumps. The scale functions express as convolution series of the usual scale functions associated with spectrally one-sided L\\'evy processes that underly the pssMp through the Lamperti transform. This theory is then brought to bear on solving the spatio-temporal: (i) two-sided exit problem; (ii) joint first passage problem upwards for the the pssMp and its multiplicative drawdown (resp. drawup) in the spectrally negative (resp. positive) case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-02T06:39:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60G18",
      "60G44"
    ],
    "keywords": [
      "positive self-similar markov processes",
      "exit problem",
      "one-sided jumps",
      "usual scale functions",
      "joint first passage problem upwards"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}