{
  "id": "1701.03870",
  "version": "v1",
  "published": "2017-01-14T02:13:49.000Z",
  "updated": "2017-01-14T02:13:49.000Z",
  "title": "A representation theorem for generators of BSDEs with general growth generators in $y$ and its applications",
  "authors": [
    "Lishun Xiao",
    "Shengjun Fan"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we first prove a general representation theorem for generators of backward stochastic differential equations (BSDEs for short) by utilizing a localization method involved with stopping time tools and approximation techniques, where the generators only need to satisfy a weak monotonicity condition and a general growth condition in $y$ and a Lipschitz condition in $z$. This result basically solves the problem of representation theorems for generators of BSDEs with general growth generators in $y$. Then, such representation theorem is adopted to prove a probabilistic formula, in viscosity sense, of semilinear parabolic PDEs of second order. The representation theorem approach seems to be a potential tool to the research of viscosity solutions of PDEs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-14T02:13:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "35K58"
    ],
    "keywords": [
      "general growth generators",
      "applications",
      "representation theorem approach",
      "general representation theorem",
      "backward stochastic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}