{
  "id": "1609.02438",
  "version": "v1",
  "published": "2016-09-08T14:08:33.000Z",
  "updated": "2016-09-08T14:08:33.000Z",
  "title": "Integration by parts on the law of the modulus of the Brownian bridge",
  "authors": [
    "Martin Grothaus",
    "Robert Voßhall"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We prove an infinite dimensional integration by parts formula on the law of the modulus of the Brownian bridge $BB=(BB_t)_{0 \\leq t \\leq 1}$ from $0$ to $0$ in use of methods from white noise analysis and Dirichlet form theory. Additionally to the usual drift term, this formula contains a distribution which is constructed in the space of Hida distributions in use of a Wick product with Donsker's delta (which correlates with the local time of $|BB|$ at zero). This additional distribution corresponds to the reflection at zero caused by the modulus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-08T14:08:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60H40",
      "46F25",
      "31C25"
    ],
    "keywords": [
      "brownian bridge",
      "additional distribution corresponds",
      "white noise analysis",
      "dirichlet form theory",
      "usual drift term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}