{
  "id": "1501.00698",
  "version": "v1",
  "published": "2015-01-04T17:38:00.000Z",
  "updated": "2015-01-04T17:38:00.000Z",
  "title": "Maximal inequalities for centered norms of sums of independent random vectors",
  "authors": [
    "Rafał Latała"
  ],
  "comment": "9 pages",
  "journal": "High Dimensional Probability VI, The Banff Volume, Progr. Probab. 66, 63-71, Birkhauser 2013",
  "doi": "10.1007/978-3-0348-0490-5_4",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $X_1,X_2,\\ldots,X_n$ be independent random variables and $S_k=\\sum_{i=1}^k X_i$. We show that for any constants $a_k$, \\[ \\Pr(\\max_{1\\leq k\\leq n}||S_{k}|-a_{k}|>11t)\\leq 30 \\max_{1\\leq k\\leq n}\\Pr(||S_{k}|-a_{k}|>t). \\] We also discuss similar inequalities for sums of Hilbert and Banach space valued random vectors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-04T17:38:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15"
    ],
    "keywords": [
      "independent random vectors",
      "maximal inequalities",
      "centered norms",
      "banach space valued random vectors",
      "independent random variables"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}