{
  "id": "0909.3385",
  "version": "v1",
  "published": "2009-09-18T08:38:19.000Z",
  "updated": "2009-09-18T08:38:19.000Z",
  "title": "Convergence of a kinetic equation to a fractional diffusion equation",
  "authors": [
    "Giada Basile",
    "Anton Bovier"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), Y(t)), where K(t) is a autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance, while Y(t) is an additive functional of K(t). We prove that under a suitable rescaling the process Y converges in distribution to a Levy process, stable with index 3/2. Moreover, the solution of the linear Boltzmann equation converges to the solution of a fractional diffusion equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-18T08:38:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J05",
      "60G51"
    ],
    "keywords": [
      "fractional diffusion equation",
      "kinetic equation",
      "convergence",
      "linear boltzmann equation converges",
      "finite expectation value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.3385B"
    }
  }
}