{
  "id": "math/0601243",
  "version": "v1",
  "published": "2006-01-11T10:31:49.000Z",
  "updated": "2006-01-11T10:31:49.000Z",
  "title": "On some transformations between positive self--similar Markov processes",
  "authors": [
    "Loïc Chaumont",
    "Víctor Manuel Rivero"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "A path decomposition at the infimum for positive self-similar Markov processes (pssMp) is obtained. Next, several aspects of the conditioning to hit 0 of a pssMp are studied. Associated to a given a pssMp $X,$ that never hits 0, we construct a pssMp $X^{\\downarrow}$ that hits 0 in a finite time. The latter can be viewed as $X$ conditioned to hit 0 in a finite time and we prove that this conditioning is determined by the pre-minimum part of $X.$ Finally, we provide a method for conditioning a pssMp that hits 0 by a jump to do it continuously.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-11T10:31:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G18",
      "60G17"
    ],
    "keywords": [
      "positive self-similar markov processes",
      "transformations",
      "finite time",
      "path decomposition",
      "pre-minimum part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1243C"
    }
  }
}