{
  "id": "1602.01309",
  "version": "v1",
  "published": "2016-02-03T14:15:52.000Z",
  "updated": "2016-02-03T14:15:52.000Z",
  "title": "Continuity of the Feynman-Kac formula for a generalized parabolic equation",
  "authors": [
    "Etienne Pardoux",
    "Aurel Rascanu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "It is well-known since the work of Pardoux and Peng [12] that Backward Stochastic Differential Equations provide probabilistic formulae for the solution of (systems of) second order elliptic and parabolic equations, thus providing an extension of the Feynman-Kac formula to semilinear PDEs, see also Pardoux and Rascanu [14]. This method was applied to the class of PDEs with a nonlinear Neumann boundary condition first by Pardoux and Zhang [15]. However, the proof of continuity of the extended Feynman-Kac formula with respect to x (resp. to (t,x)) is not correct in that paper. Here we consider a more general situation, where both the equation and the boundary condition involve the (possibly multivalued) gradient of a convex function. We prove the required continuity. The result for the class of equations studied in [15] is a Corollary of our main results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-03T14:15:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "feynman-kac formula",
      "generalized parabolic equation",
      "continuity",
      "nonlinear neumann boundary condition first",
      "backward stochastic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160201309P"
    }
  }
}