{
  "id": "0902.3536",
  "version": "v3",
  "published": "2009-02-20T08:50:53.000Z",
  "updated": "2009-09-20T14:39:59.000Z",
  "title": "Levy flights and Levy -Schroedinger semigroups",
  "authors": [
    "Piotr Garbaczewski"
  ],
  "comment": "To appear in Cent. Eur. J. Phys. (2010)",
  "journal": "Cent. Eur. J. Phys, 8(5), 699-708, (2010)",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We analyze two different confining mechanisms for L\\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\\'{e}vy process with the very same invariant pdf and in the reverse.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-09-20T14:39:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "levy flights",
      "langevin-based fractional fokker-planck equation",
      "stationary probability function",
      "invariant pdf",
      "external potentials"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.2478/s11534-009-0156-z",
      "journal": "Central European Journal of Physics",
      "year": 2010,
      "month": "Oct",
      "volume": 8,
      "number": 5,
      "pages": 699
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010CEJPh...8..699G"
    }
  }
}