{
  "id": "math/0610485",
  "version": "v1",
  "published": "2006-10-16T14:07:08.000Z",
  "updated": "2006-10-16T14:07:08.000Z",
  "title": "Differential calculus for Dirichlet forms : the measure-valued gradient preserved by image",
  "authors": [
    "Nicolas Bouleau"
  ],
  "journal": "Journal of Functional Analysis 225 (2005) 63-73",
  "categories": [
    "math.PR"
  ],
  "abstract": "In order to develop a differential calculus for error propagation we study local Dirichlet forms on probability spaces with square field operator $\\Gamma$ -- i.e. error structures -- and we are looking for an object related to $\\Gamma$ which is linear and with a good behaviour by images. For this we introduce a new notion called the measure valued gradient which is a randomized square root of $\\Gamma$. The exposition begins with inspecting some natural notions candidate to solve the problem before proposing the measure-valued gradient and proving its satisfactory properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-16T14:07:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C25",
      "65G99",
      "60H07"
    ],
    "keywords": [
      "differential calculus",
      "measure-valued gradient",
      "study local dirichlet forms",
      "square field operator",
      "natural notions candidate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10485B"
    }
  }
}