{
  "id": "1108.3246",
  "version": "v1",
  "published": "2011-08-16T14:20:59.000Z",
  "updated": "2011-08-16T14:20:59.000Z",
  "title": "Some Theorems on Feller Processes: Transience, Local Times and Ultracontractivity",
  "authors": [
    "René L. Schilling",
    "Jian Wang"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present sufficient conditions for the transience and the existence of local times of a Feller process, and the ultracontractivity of the associated Feller semigroup; these conditions are sharp for L\\'{e}vy processes. The proof uses a local symmetrization technique and a uniform upper bound for the characteristic function of a Feller process. As a byproduct, we obtain for stable-like processes (in the sense of R.\\ Bass) on $\\R^d$ with smooth variable index $\\alpha(x)\\in(0,2)$ a transience criterion in terms of the exponent $\\alpha(x)$; if $d=1$ and $\\inf_{x\\in\\R} \\alpha(x)\\in (1,2)$, then the stable-like process has local times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-16T14:20:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60J75",
      "35S05"
    ],
    "keywords": [
      "local times",
      "feller processes",
      "ultracontractivity",
      "uniform upper bound",
      "local symmetrization technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.3246S"
    }
  }
}