{
  "id": "1705.02830",
  "version": "v1",
  "published": "2017-05-08T11:25:47.000Z",
  "updated": "2017-05-08T11:25:47.000Z",
  "title": "Random time changes of Feller processes",
  "authors": [
    "Franziska Kühn"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that the SDE $dX_t = \\sigma(X_{t-}) \\, dL_t$, $X_0 \\sim \\mu$ driven by a one-dimensional symnmetric $\\alpha$-stable L\\'evy process $(L_t)_{t \\geq 0}$, $\\alpha \\in (0,2]$, has a unique weak solution for any continuous function $\\sigma: \\mathbb{R} \\to (0,\\infty)$ which grows at most linearly. Our approach relies on random time changes of Feller processes. We study under which assumptions the random-time change of a Feller process is a conservative $C_b$-Feller process and prove the existence of a class of Feller processes with decomposable symbols. In particular, we establish new existence results for Feller processes with unbounded coefficients. As a by-product, we obtain a sufficient condition in terms of the symbol of a Feller process $(X_t)_{t \\geq 0}$ for the perpetual integral $\\int_{(0,\\infty)} f(X_{s}) \\, ds$ to be infinite almost surely.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-08T11:25:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60H10",
      "60G51",
      "60J75",
      "60J35",
      "60G44"
    ],
    "keywords": [
      "feller process",
      "random time changes",
      "unique weak solution",
      "one-dimensional symnmetric",
      "stable levy process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}