{
  "id": "1506.07358",
  "version": "v1",
  "published": "2015-06-24T13:12:23.000Z",
  "updated": "2015-06-24T13:12:23.000Z",
  "title": "A limit theorem for the $L^p$-modulus of continuity of Brownian local time",
  "authors": [
    "Simon Campese"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We proof a limit theorem for the $L^p$-modulus of continuity of Brownian local time. As special cases for $p=2$ and $p=3$, we obtain previous results by Chen et al. (Ann. Prob. 38, 2010, no. 1) and Rosen~(Stoch. Dyn. 11, 2011, no. 1), which were later reproven by Hu and Nualart~(Electron. Commun. Probab. 14, 2009; Electron. Commun. Probab. 15, 2010) and Rosen~(S\\'eminaire de Probabilit\\'es XLIII, Springer, 2011). In comparison to the previous methods of proof, we follow a fundamentally different approach by exclusively working in the space variable of the Brownian local time, which allows to give a unified argument for arbitrary integer power $p$. The main ingredients are Perkins' semimartingale decomposition, the Kailath-Segall identity and an asymptotic Ray-Knight Theorem by Pitman and Yor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-24T13:12:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G44",
      "60H05"
    ],
    "keywords": [
      "brownian local time",
      "limit theorem",
      "continuity",
      "arbitrary integer power",
      "asymptotic ray-knight theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607358C"
    }
  }
}