{
  "id": "1003.0661",
  "version": "v2",
  "published": "2010-03-02T19:45:49.000Z",
  "updated": "2011-06-15T09:43:59.000Z",
  "title": "Almost sure asymptotics for the maximum local time in Brownian environment",
  "authors": [
    "Roland Diel"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic behaviour of the maximum local time L*(t) of the Brox's process, the diffusion in Brownian environment. Shi proved that the maximum speed of L*(t) is surprisingly, at least t log(log(log t)) whereas in the discrete case it is t. We show here that t log(log(log t)) is the proper rate and we prove that for the minimum speed the rate is the same as in the discrete case namely t/log(log(log t)).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-15T09:43:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum local time",
      "brownian environment",
      "sure asymptotics",
      "discrete case",
      "broxs process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.0661D"
    }
  }
}