{
  "id": "math/0312455",
  "version": "v2",
  "published": "2003-12-25T06:23:49.000Z",
  "updated": "2007-12-20T12:59:00.000Z",
  "title": "The divergence of Banach space valued random variables on Wiener space",
  "authors": [
    "E. Mayer-Wolf",
    "M. Zakai"
  ],
  "comment": "an arXiv link to a corrigendum has been added, see arXiv:0710.4483",
  "journal": "Probability Theory and Related Fields, vol. 132, no. 2, pp. 291-320, June 2005",
  "categories": [
    "math.PR"
  ],
  "abstract": "The domain of definition of the divergence operator \\delta on an abstract Wiener space (W, H, \\mu) is extended to include W-valued and W\\otimesW-valued \"integrands\". The main properties and characterizations of this extension are derived and it is shown that in some sense the added elements in \\delta's extended domain have divergence zero. These results are then applied to the analysis of quasiinvariant flows induced by W-valued vector fields and, among other results, it turns out that these divergence-free vector fields \"are responsible\" for generating measure preserving flows.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-12-20T12:59:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60H05"
    ],
    "keywords": [
      "banach space valued random variables",
      "abstract wiener space",
      "divergence-free vector fields",
      "main properties",
      "divergence operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12455M"
    }
  }
}