{
  "id": "1308.4194",
  "version": "v1",
  "published": "2013-08-20T00:17:15.000Z",
  "updated": "2013-08-20T00:17:15.000Z",
  "title": "Empirical Quantile CLTs For Some Self-Similar Processes",
  "authors": [
    "James Kuelbs",
    "Joel Zinn"
  ],
  "comment": "24 pages. arXiv admin note: text overlap with arXiv:1111.4591",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "In a paper of Jason Swanson, a CLT for the sample median of independent Brownian motions with value 0 at 0 was proved. Here we extend this result in two ways. We prove such a result for a collection of self-similar processes which include the fractional Brownian motions, all stationary, independent increment symmetric stable processes tied down at 0 as well as iterated and integrated Brownian motions. Second, our results hold uniformly over all quantiles in a compact sub-interval of (0,1). We also examine sample function properties connected with these CLTs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-20T00:17:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60F17",
      "62E20"
    ],
    "keywords": [
      "self-similar processes",
      "empirical quantile clts",
      "independent increment symmetric stable processes",
      "independent brownian motions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.4194K"
    }
  }
}