{
  "id": "1101.3038",
  "version": "v3",
  "published": "2011-01-16T01:47:55.000Z",
  "updated": "2012-12-11T04:34:09.000Z",
  "title": "Hunt's hypothesis (H) and Getoor's conjecture for Lévy Processes",
  "authors": [
    "Ze-Chun Hu",
    "Wei Sun"
  ],
  "comment": "11 pages. arXiv admin note: text overlap with arXiv:1210.2016",
  "journal": "Stochastic Processes and their Applications 122 (2012) 2319-2328",
  "doi": "10.1016/j.spa.2012.03.013",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, Hunt's hypothesis (H) and Getoor's conjecture for L\\'{e}vy processes are revisited. Let $X$ be a L\\'{e}vy process on $\\mathbf{R}^n$ with L\\'{e}vy-Khintchine exponent $(a,A,\\mu)$. {First, we show that if $A$ is non-degenerate then $X$ satisfies (H). Second, under the assumption that $\\mu({\\mathbf{R}^n\\backslash \\sqrt{A}\\mathbf{R}^n})<\\infty$, we show that $X$ satisfies (H) if and only if the equation $$ \\sqrt{A}y=-a-\\int_{\\{x\\in {\\mathbf{R}^n\\backslash \\sqrt{A}\\mathbf{R}^n}:\\,|x|<1\\}}x\\mu(dx),\\ y\\in \\mathbf{R}^n, $$ has at least one solution. Finally, we show that if $X$ is a subordinator and satisfies (H) then its drift coefficient must be 0.}",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-11T04:34:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J45",
      "60G51"
    ],
    "keywords": [
      "getoors conjecture",
      "hunts hypothesis",
      "lévy processes",
      "drift coefficient",
      "non-degenerate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.3038H"
    }
  }
}