{
  "id": "1109.5971",
  "version": "v2",
  "published": "2011-09-27T17:02:09.000Z",
  "updated": "2014-01-14T09:02:31.000Z",
  "title": "On viscosity solutions of path dependent PDEs",
  "authors": [
    "Ibrahim Ekren",
    "Christian Keller",
    "Nizar Touzi",
    "Jianfeng Zhang"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/12-AOP788 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2014, Vol. 42, No. 1, 204-236",
  "doi": "10.1214/12-AOP788",
  "categories": [
    "math.AP",
    "math.FA",
    "math.PR"
  ],
  "abstract": "In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian backward SDEs, and thus extends the well-known nonlinear Feynman-Kac formula to non-Markovian case. We shall prove the existence, uniqueness, stability and comparison principle for the viscosity solutions. The key ingredient of our approach is a functional It\\^{o} calculus recently introduced by Dupire [Functional It\\^{o} calculus (2009) Preprint].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-14T09:02:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "viscosity solutions",
      "path dependent pdes",
      "path dependent semi-linear parabolic pdes",
      "well-known nonlinear feynman-kac formula",
      "non-markovian backward sdes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.5971E"
    }
  }
}