{
  "id": "0712.3635",
  "version": "v1",
  "published": "2007-12-21T07:51:40.000Z",
  "updated": "2007-12-21T07:51:40.000Z",
  "title": "Convergence Rates for Approximations of Functionals of SDEs",
  "authors": [
    "Rainer Avikainen"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider upper bounds for the approximation error E|g(X)-g(\\hat X)|^p, where X and \\hat X are random variables such that \\hat X is an approximation of X in the L_p-norm, and the function g belongs to certain function classes, which contain e.g. functions of bounded variation. We apply the results to the approximations of a solution of a stochastic differential equation at time T by the Euler and Milstein schemes. For the Euler scheme we provide also a lower bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-21T07:51:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "41A25",
      "26A45",
      "65C20",
      "65C30"
    ],
    "keywords": [
      "convergence rates",
      "functionals",
      "stochastic differential equation",
      "approximation error",
      "function classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3635A"
    }
  }
}