{
  "id": "math/0406557",
  "version": "v1",
  "published": "2004-06-28T06:00:59.000Z",
  "updated": "2004-06-28T06:00:59.000Z",
  "title": "Brownian Sheet and Quasi-Sure Analysis",
  "authors": [
    "Davar Khoshnevisan"
  ],
  "comment": "23 pages. Proceedings of the Fields Institute (to appear)",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present a self-contained and modern survey of some existing quasi-sure results via the connection to the Brownian sheet. Among other things, we prove that quasi-every continuous function: (i) satisfies the local law of the iterated logarithm; (ii) has Levy's modulus of continuity for Brownian motion; (iii) is nowhere differentiable; and (iv) has a nontrivial quadratic variation. We also present a hint of how to extend (iii) to obtain a quasi-sure refinement of the M. Csorgo--P. Revesz modulus of continuity for almost every continuous function along the lines suggested by M. Fukushima.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-28T06:00:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60-02"
    ],
    "keywords": [
      "brownian sheet",
      "quasi-sure analysis",
      "nontrivial quadratic variation",
      "revesz modulus",
      "existing quasi-sure results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6557K"
    }
  }
}