{
  "id": "1310.1173",
  "version": "v2",
  "published": "2013-10-04T05:55:17.000Z",
  "updated": "2015-09-09T06:36:59.000Z",
  "title": "Weak approximation of second-order BSDEs",
  "authors": [
    "Dylan Possamaï",
    "Xiaolu Tan"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/14-AAP1055 in 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 2015, Vol. 25, No. 5, 2535-2562",
  "doi": "10.1214/14-AAP1055",
  "categories": [
    "math.PR",
    "math.NA"
  ],
  "abstract": "We study the weak approximation of the second-order backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time martingales. We establish a convergence result for a class of 2BSDEs, using both robustness properties of BSDEs, as proved in Briand, Delyon and M\\'{e}min [Stochastic Process. Appl. 97 (2002) 229-253], and tightness of solutions to discrete time BSDEs. In particular, when the approximating martingales are given by some particular controlled Markov chains, we obtain several concrete numerical schemes for 2BSDEs, which we illustrate on specific examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-04T05:55:17.000Z",
      "title": "Weak approximation of second order BSDEs",
      "abstract": "We study the weak approximation of the second order Backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time martingales. We establish a convergence result for a class of 2BSDEs, using both robustness properties of BSDEs, as proved in Briand, Delyon and M\\'emin [7], and tightness of solutions to discrete time BSDEs. In particular, when the approximating martingales are given by some particular controlled Markov chains, we obtain several concrete numerical schemes for 2BSDEs.",
      "comment": "23 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-09T06:36:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second order bsdes",
      "weak approximation",
      "discrete time bsdes",
      "discrete time martingales",
      "second order backward sdes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.1173P"
    }
  }
}