{
  "id": "1202.4625",
  "version": "v1",
  "published": "2012-02-21T12:45:24.000Z",
  "updated": "2012-02-21T12:45:24.000Z",
  "title": "Malliavin calculus for backward stochastic differential equations and application to numerical solutions",
  "authors": [
    "Yaozhong Hu",
    "David Nualart",
    "Xiaoming Song"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/11-AAP762 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2011, Vol. 21, No. 6, 2379-2423",
  "doi": "10.1214/11-AAP762",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The randomness of the generator does not need to be from a forward equation, either. Motivated from applications to numerical simulations, first we obtain the $L^p$-H\\\"{o}lder continuity of the solution. Then we construct several numerical approximation schemes for backward stochastic differential equations and obtain the rate of convergence of the schemes based on the obtained $L^p$-H\\\"{o}lder continuity results. The main tool is the Malliavin calculus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-21T12:45:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "malliavin calculus",
      "numerical solutions",
      "application",
      "study backward stochastic differential equations",
      "general random generator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}