{
  "id": "1104.1192",
  "version": "v4",
  "published": "2011-04-06T20:42:31.000Z",
  "updated": "2013-08-19T19:28:52.000Z",
  "title": "Weak solutions of backward stochastic differential equations with continuous generator",
  "authors": [
    "Nadira Bouchemella",
    "Paul Raynaud De Fitte"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove the existence of a weak solution to a backward stochastic differential equation (BSDE) $$ Y_t=\\xi+\\int_t^T f(s,X_s,Y_s,Z_s)\\,ds-\\int_t^T Z_s\\,d\\wien_s$$ in a finite-dimensional space, where $f(t,x,y,z)$ is affine with respect to $z$, and satisfies a sublinear growth condition and a continuity condition This solution takes the form of a triplet $(Y,Z,L)$ of processes defined on an extended probability space and satisfying $$ Y_t=\\xi+\\int_t^T f(s,X_s,Y_s,Z_s)\\,ds-\\int_t^T Z_s\\,d\\wien_s-(L_T-L_t)$$ where $L$ is a continuous martingale which is orthogonal to any $\\wien$. The solution is constructed on an extended probability space, using Young measures on the space of trajectories. One component of this space is the Skorokhod space D endowed with the topology S of Jakubowski.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-08-19T19:28:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "backward stochastic differential equation",
      "weak solution",
      "continuous generator",
      "extended probability space",
      "sublinear growth condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.1192B"
    }
  }
}