{
  "id": "math/0512195",
  "version": "v1",
  "published": "2005-12-09T13:04:50.000Z",
  "updated": "2005-12-09T13:04:50.000Z",
  "title": "Feller property and infinitesimal generator of the exploration process",
  "authors": [
    "Romain Abraham",
    "Jean-Francois Delmas"
  ],
  "journal": "Journal of Theoretical Probability 20 (2007) 355-370",
  "doi": "10.1007/s10959-007-0082-1",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the exploration process associated to the continuous random tree (CRT) built using a Levy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a useful tool to study CRT as well as super-Brownian motion with general branching mechanism. In this paper we prove this process is Feller, and we compute its infinitesimal generator on exponential functionals and give the corresponding martingale.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-09T13:04:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J35",
      "60J80",
      "60G57"
    ],
    "keywords": [
      "infinitesimal generator",
      "exploration process",
      "feller property",
      "exponential functionals",
      "levy process"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12195A"
    }
  }
}