{
  "id": "1208.5196",
  "version": "v2",
  "published": "2012-08-26T07:02:34.000Z",
  "updated": "2012-09-29T09:22:40.000Z",
  "title": "Oscillation of harmonic functions for subordinate Brownian motion and its applications",
  "authors": [
    "Panki Kim",
    "Yunju Lee"
  ],
  "comment": "24pages. To appear in Stochastic Processes and their Applications (http://www.journals.elsevier.com/stochastic-processes-and-their-applications)",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we establish an oscillation estimate of nonnegative harmonic functions for a pure-jump subordinate Brownian motion. The infinitesimal generator of such subordinate Brownian motion is an integro-differential operator. As an application, we give a probabilistic proof of the following form of relative Fatou theorem for such subordinate Brownian motion X in bounded kappa-fat open set; if u is a positive harmonic function with respect to X in a bounded kappa-fat open set D and h is a positive harmonic function in D vanishing on D^c, then the non-tangential limit of u/h exists almost everywhere with respect to the Martin-representing measure of h.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-29T09:22:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded kappa-fat open set",
      "application",
      "positive harmonic function",
      "oscillation",
      "pure-jump subordinate brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.5196K"
    }
  }
}