{
  "id": "1507.02846",
  "version": "v1",
  "published": "2015-07-10T11:00:18.000Z",
  "updated": "2015-07-10T11:00:18.000Z",
  "title": "Tail probabilities of St. Petersburg sums, trimmed sums, and their limit",
  "authors": [
    "István Berkes",
    "László Györfi",
    "Péter Kevei"
  ],
  "comment": "24 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We provide exact asymptotics for the tail probabilities $\\mathbb{P} \\{S_{n,r} > x\\}$ as $x \\to \\infty$, for fix $n$, where $S_{n,r}$ is the $r$-trimmed partial sum of i.i.d. St. Petersburg random variables. In particular, we prove that although the St. Petersburg distribution is only O-subexponential, the subexponential property almost holds. We also determine the exact tail behavior of the $r$-trimmed limits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-10T11:00:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60E07"
    ],
    "keywords": [
      "tail probabilities",
      "petersburg sums",
      "trimmed sums",
      "exact tail behavior",
      "petersburg random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}