{
  "id": "1809.08569",
  "version": "v1",
  "published": "2018-09-23T09:59:43.000Z",
  "updated": "2018-09-23T09:59:43.000Z",
  "title": "Bounds on tail probabilities for quadratic forms in dependent sub-gaussian random variables",
  "authors": [
    "Krzysztof Zajkowski"
  ],
  "comment": "9 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show bounds on tail probabilities for quadratic forms in sub-gaussian not necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned bounds. As an example we give estimates of tail probabilities for quadratic forms in bounded martingale increments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-23T09:59:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60F10"
    ],
    "keywords": [
      "dependent sub-gaussian random variables",
      "tail probabilities",
      "quadratic forms",
      "necessarily independent random variables",
      "luxemburg norms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}