{
  "id": "1008.4341",
  "version": "v1",
  "published": "2010-08-25T19:09:59.000Z",
  "updated": "2010-08-25T19:09:59.000Z",
  "title": "A Refinement of the Kolmogorov-Marcinkiewicz-Zygmund Strong Law of Large Numbers",
  "authors": [
    "Deli Li",
    "Yongcheng Qi",
    "Andrew Rosalsky"
  ],
  "comment": "26 pages. To appear in the Journal of Theoretical Probability",
  "categories": [
    "math.PR"
  ],
  "abstract": "For the partial sums formed from a sequence of i.i.d. random variables having a finite absolute p'th moment for some p in (0,2), we extend the recent and striking discovery of Hechner and Heinkel (Journal of Theoretical Probability (2010)) concerning \"complete moment convergence\" to the two cases 0<p<1 and p=1. Moreover, for 0<p<2, we obtain \"almost sure convergence\" analogues of these \"complete moment convergence\" results and these \"almost sure convergence\" analogues may be regarded as being a refinement of the celebrated Kolmogorov-Marcinkiewicz-Zygmund strong law of large numbers. Versions of the above results in a Banach space setting are also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-25T19:09:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15",
      "60B12",
      "60G50"
    ],
    "keywords": [
      "large numbers",
      "complete moment convergence",
      "refinement",
      "sure convergence",
      "finite absolute pth moment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.4341L"
    }
  }
}