{
  "id": "1212.2325",
  "version": "v1",
  "published": "2012-12-11T08:08:28.000Z",
  "updated": "2012-12-11T08:08:28.000Z",
  "title": "Long-time behavior of stable-like processes",
  "authors": [
    "Nikola Sandrić"
  ],
  "comment": "To appear in: Stochastic Processes and their Applications",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol $p(x,\\xi)=-i\\beta(x)\\xi+\\gamma(x)|\\xi|^{\\alpha(x)},$ where $\\alpha(x)\\in(0,2)$, $\\beta(x)\\in\\R$ and $\\gamma(x)\\in(0,\\infty)$. More precisely, we give sufficient conditions for recurrence, transience and ergodicity of stable-like processes in terms of the stability function $\\alpha(x)$, the drift function $\\beta(x)$ and the scaling function $\\gamma(x)$. Further, as a special case of these results we give a new proof for the recurrence and transience property of one-dimensional symmetric stable L\\'{e}vy processes with the index of stability $\\alpha\\neq1.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-11T08:08:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60J75",
      "60G52"
    ],
    "keywords": [
      "stable-like processes",
      "long-time behavior",
      "sufficient conditions",
      "recurrence",
      "one-dimensional symmetric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.2325S"
    }
  }
}