{
  "id": "1302.2435",
  "version": "v1",
  "published": "2013-02-11T10:19:40.000Z",
  "updated": "2013-02-11T10:19:40.000Z",
  "title": "Comparison for upper tail probabilities of random series",
  "authors": [
    "Fuchang Gao",
    "Zhenxia Liu",
    "Xiangfeng Yang"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\{\\xi_n\\}$ be a sequence of independent and identically distributed random variables. In this paper we study the comparison for two upper tail probabilities $\\mathbb{P}\\{\\sum_{n=1}^{\\infty}a_n|\\xi_n|^p\\geq r\\}$ and $\\mathbb{P}\\{\\sum_{n=1}^{\\infty}b_n|\\xi_n|^p\\geq r\\}$ as $r\\rightarrow\\infty$ with two different real series $\\{a_n\\}$ and $\\{b_n\\}.$ The first result is for Gaussian random variables $\\{\\xi_n\\},$ and in this case these two probabilities are equivalent after suitable scaling. The second result is for more general random variables, thus a weaker form of equivalence (namely, logarithmic level) is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-11T10:19:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G50"
    ],
    "keywords": [
      "upper tail probabilities",
      "random series",
      "comparison",
      "general random variables",
      "gaussian random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.2435G"
    }
  }
}