{
  "id": "1307.7158",
  "version": "v1",
  "published": "2013-07-26T20:22:21.000Z",
  "updated": "2013-07-26T20:22:21.000Z",
  "title": "Gradient estimates of harmonic functions and transition densities for Levy processes",
  "authors": [
    "Tadeusz Kulczycki",
    "Michal Ryznar"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove gradient estimates for harmonic functions with respect to a $d$-dimensional unimodal pure-jump Levy process under some mild assumptions on the density of its Levy measure. These assumptions allow for a construction of an unimodal Levy process in $\\R^{d+2}$ with the same characteristic exponent as the original process. The relationship between the two processes provides a fruitful source of gradient estimates of transition densities. We also construct another process called a difference process which is very useful in the analysis of differential properties of harmonic functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-26T20:22:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic functions",
      "gradient estimates",
      "transition densities",
      "levy processes",
      "dimensional unimodal pure-jump levy process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7158K"
    }
  }
}