{
  "id": "1703.02007",
  "version": "v1",
  "published": "2017-03-06T18:13:52.000Z",
  "updated": "2017-03-06T18:13:52.000Z",
  "title": "Numerical Method for FBSDEs of McKean-Vlasov Type",
  "authors": [
    "Jean-François Chassagneux",
    "Dan Crisan",
    "François Delarue"
  ],
  "comment": "33 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper is dedicated to the presentation and the analysis of a numerical scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for solutions to PDEs on the Wasserstein space. Because of the mean field structure of the equation, earlier methods for classical forward-backward systems fail. The scheme is based on a variation of the method of continuation. The principle is to implement recursively local Picard iterations on small time intervals. We establish a bound for the rate of convergence under the assumption that the decoupling field of the forward-bakward SDE (or equivalently the solution of the PDE) satisfies mild regularity conditions. We also provide numerical illustrations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-06T18:13:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mckean-vlasov type",
      "numerical method",
      "satisfies mild regularity conditions",
      "implement recursively local picard iterations",
      "small time intervals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}