{
  "id": "0912.1458",
  "version": "v3",
  "published": "2009-12-08T10:55:10.000Z",
  "updated": "2010-12-01T10:37:33.000Z",
  "title": "The Symbol Associated with the Solution of a Stochastic Differential Equation",
  "authors": [
    "Rene L. Schilling",
    "Alexander Schnurr"
  ],
  "comment": "21 pages",
  "journal": "Electr. J. Probab. 15 (2010), 1369-1393",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a stochastic differential equations which is driven by a Levy process. It turns out that the solution process is a Feller process if the coefficient of the SDE is bounded. Using a probabilistic formula we calculate the symbol, which appears in the Fourier representation of the generator, explicitely. Using the symbol we introduce indices which are generalizations of the well known Blumenthal-Getoor index. These indices are then used to obtain some fine properties of the solution process.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-12-01T10:37:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J75",
      "47G30",
      "60H20",
      "60J25",
      "60G51",
      "60G17"
    ],
    "keywords": [
      "stochastic differential equation",
      "solution process",
      "feller process",
      "fine properties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1458S"
    }
  }
}