{
  "id": "1408.1426",
  "version": "v2",
  "published": "2014-08-06T21:16:01.000Z",
  "updated": "2014-08-24T05:21:26.000Z",
  "title": "A Note on the sharp $L^p$-Covergence rate of Upcrossings to the Brownian local time",
  "authors": [
    "Alberto Ohashi",
    "Alexandre B. Simas"
  ],
  "comment": "Some typos are corrected",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note, we prove a sharp $L^p$-rate of convergence of the number of upcrossings to the local time of the Brownian motion. In particular, it provides novel $p$-variation estimates ($2 < p < \\infty$) for the number of upcrossings of the Brownian motion. Our result complements the fundamental work of Koshnevisan \\cite{kho} who obtains an almost sure exact rate of convergence in the sup norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-06T21:16:01.000Z",
      "abstract": "In this note, we prove a sharp $L^p$-rate of convergence of the number of upcrossings to the local time of the Brownian motion. In particular, it provides novel $p$-variation estimates ($2 < p < \\infty$) for the number of upcrossings. Our result complements the fundamental work of Koshnevisan \\cite{kho} who obtains an almost sure exact rate of convergence in the sup norm.",
      "comment": "7 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-24T05:21:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian local time",
      "covergence rate",
      "upcrossings",
      "sure exact rate",
      "brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.1426O"
    }
  }
}