{
  "id": "1303.6449",
  "version": "v1",
  "published": "2013-03-26T12:05:23.000Z",
  "updated": "2013-03-26T12:05:23.000Z",
  "title": "Dirichlet Heat Kernel Estimates for Rotationally Symmetric Lévy processes",
  "authors": [
    "Zhen-Qing Chen",
    "Panki Kim",
    "Renming Song"
  ],
  "comment": "1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we consider a large class of purely discontinuous rotationally symmetric Levy processes. We establish sharp two-sided estimates for the transition densities of such processes killed upon leaving an open set D. When D is a \\kappa-fat open set, the sharp two-sided estimates are given in terms of surviving probabilities and the global transition density of the Levy process. When D is a C^{1, 1} open set and the Levy exponent of the process is given by \\Psi(\\xi)= \\phi(|\\xi|^2) with \\phi being a complete Bernstein function satisfying a mild growth condition at infinity, our two-sided estimates are explicit in terms of \\Psi, the distance function to the boundary of D and the jumping kernel of X, which give an affirmative answer to the conjecture posted in [Potential Anal., 36 (2012) 235-261]. Our results are the first sharp two-sided Dirichlet heat kernel estimates for a large class of symmetric Levy processes with general Levy exponents. We also derive an explicit lower bound estimate for symmetric Levy processes on R^d in terms of their Levy exponents.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-26T12:05:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J35",
      "47G20",
      "60J75",
      "47D07",
      "60J35",
      "47G20",
      "60J75",
      "47D07"
    ],
    "keywords": [
      "dirichlet heat kernel estimates",
      "rotationally symmetric lévy processes",
      "symmetric levy processes",
      "two-sided dirichlet heat",
      "rotationally symmetric levy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.6449C"
    }
  }
}