{
  "id": "2309.12654",
  "version": "v1",
  "published": "2023-09-22T06:51:31.000Z",
  "updated": "2023-09-22T06:51:31.000Z",
  "title": "Some extreme value theory for $θ$-expansions",
  "authors": [
    "Gabriela Ileana Sebe",
    "Dan Lascu"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR",
    "math.NT"
  ],
  "abstract": "The main aim of this paper is to develop extreme value theory for $\\theta$-expansions. We get the limit distribution of the largest value of $\\theta$-continued fraction mixing stationary stochastic process and some related results. These are analogous to J.Galambos and W.Philipp theorems for the regular continued fractions. We also have to note that a Borel-Bernstein type theorem plays an important role.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-22T06:51:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extreme value theory",
      "expansions",
      "fraction mixing stationary stochastic process",
      "borel-bernstein type theorem plays",
      "continued fraction mixing stationary stochastic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}