{
  "id": "0910.4911",
  "version": "v1",
  "published": "2009-10-26T15:59:03.000Z",
  "updated": "2009-10-26T15:59:03.000Z",
  "title": "Martingale representations for diffusion processes and backward stochastic differential equations",
  "authors": [
    "Zhongmin Qian",
    "; Jiangang Ying"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we explain that the natural filtration of a continuous Hunt process is continuous, and show that martingales over such a filtration are continuous. We further establish a martingale representation theorem for a class of continuous Hunt processes under certain technical conditions. In particular we establish the martingale representation theorem for the martingale parts of (reflecting) symmetric diffusions in a bounded domain with a continuous boundary. Together with an approach put forward in Lyons et al(2009), our martingale representation theorem is then applied to the study of initial and boundary problems for quasi-linear parabolic equations by using solutions to backward stochastic differential equations over the filtered probability space determined by reflecting diffusions in a bounded domain with only continuous boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-26T15:59:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H30",
      "60J45"
    ],
    "keywords": [
      "backward stochastic differential equations",
      "martingale representation theorem",
      "diffusion processes",
      "quasi-linear parabolic equations",
      "continuous hunt"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.4911Q"
    }
  }
}