{
  "id": "1802.09853",
  "version": "v1",
  "published": "2018-02-27T12:36:00.000Z",
  "updated": "2018-02-27T12:36:00.000Z",
  "title": "Fractional Laplacians and Levy flights in bounded domains",
  "authors": [
    "Piotr Garbaczewski"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We address L\\'{e}vy-stable stochastic processes in bounded domains, with a focus on a discrimination between inequivalent proposals for what a boundary data-respecting fractional Laplacian (and thence the induced random process) should actually be. Versions considered are: restricted Dirichlet, spectral Dirichlet and regional (censored) fractional Laplacians. The affiliated random processes comprise: killed, reflected and conditioned L\\'{e}vy flights, in particular those with an infinite life-time. The related concept of quasi-stationary distributions is briefly mentioned.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-27T12:36:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded domains",
      "levy flights",
      "boundary data-respecting fractional laplacian",
      "affiliated random processes comprise",
      "spectral dirichlet"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}