{
  "id": "1201.1049",
  "version": "v4",
  "published": "2012-01-03T21:18:24.000Z",
  "updated": "2014-04-11T14:31:05.000Z",
  "title": "Second Order Backward Stochastic Differential Equations under Monotonicity Condition",
  "authors": [
    "Dylan Possamaï"
  ],
  "comment": "29 pages, to appear in Stochastic Processes and their Applications",
  "categories": [
    "math.PR"
  ],
  "abstract": "In a recent paper, Soner, Touzi and Zhang [20] have introduced a notion of second order backward stochastic differential equations (2BSDEs for short), which are naturally linked to a class of fully non-linear PDEs. They proved existence and uniqueness for a generator which is uniformly Lipschitz in the variables $y$ and $z$. The aim of this paper is to extend these results to the case of a generator satisfying a monotonicity condition in $y$. More precisely, we prove existence and uniqueness for 2BSDEs with a generator which is Lipschitz in $z$ and uniformly continuous with linear growth in $y$. Moreover, we emphasize throughout the paper the major difficulties and differences due to the 2BSDE framework.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-04-11T14:31:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H30"
    ],
    "keywords": [
      "order backward stochastic differential equations",
      "second order backward stochastic differential",
      "monotonicity condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.1049P"
    }
  }
}