{
  "id": "1611.05993",
  "version": "v1",
  "published": "2016-11-18T07:20:08.000Z",
  "updated": "2016-11-18T07:20:08.000Z",
  "title": "On spectra of probability measures generated by GLS-expansions",
  "authors": [
    "Marina Lupain"
  ],
  "comment": "Published at http://dx.doi.org/10.15559/16-VMSTA61 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)",
  "journal": "Modern Stochastics: Theory and Applications 2016, Vol. 3, No. 3, 213-221",
  "doi": "10.15559/16-VMSTA61",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study properties of distributions of random variables with independent identically distributed symbols of generalized L\\\"{u}roth series (GLS) expansions (the family of GLS-expansions contains L\\\"{u}roth expansion and $Q_{\\infty}$- and $G_{\\infty}^2$-expansions). To this end, we explore fractal properties of the family of Cantor-like sets $C[\\mathit{GLS},V]$ consisting of real numbers whose GLS-expansions contain only symbols from some countable set $V\\subset N\\cup\\{0\\}$, and derive exact formulae for the determination of the Hausdorff--Besicovitch dimension of $C[\\mathit{GLS},V]$. Based on these results, we get general formulae for the Hausdorff--Besicovitch dimension of the spectra of random variables with independent identically distributed GLS-symbols for the case where all but countably many points from the unit interval belong to the basis cylinders of GLS-expansions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-18T07:20:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability measures",
      "gls-expansions contain",
      "hausdorff-besicovitch dimension",
      "random variables",
      "unit interval belong"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}