{
  "id": "2211.05511",
  "version": "v1",
  "published": "2022-11-10T12:08:10.000Z",
  "updated": "2022-11-10T12:08:10.000Z",
  "title": "The fractional Laplacian with reflections",
  "authors": [
    "Krzysztof Bogdan",
    "Markus Kunze"
  ],
  "comment": "26 pages, no figures",
  "categories": [
    "math.PR",
    "math.AP",
    "math.FA"
  ],
  "abstract": "Motivated by the notion of isotropic $\\alpha$-stable L\\'evy processes confined, by reflections, to a bounded open Lipschitz set $D\\subset \\mathbb{R}^d$, we study some related analytical objects. Thus, we construct the corresponding transition semigroup, identify its generator and prove exponential speed of convergence of the semigroup to a unique stationary distribution for large time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-10T12:08:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D06",
      "60J35"
    ],
    "keywords": [
      "fractional laplacian",
      "reflections",
      "bounded open lipschitz set",
      "unique stationary distribution",
      "stable levy processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}