{
  "id": "1309.7657",
  "version": "v3",
  "published": "2013-09-29T20:19:41.000Z",
  "updated": "2016-11-20T02:37:58.000Z",
  "title": "Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations",
  "authors": [
    "Martin Hutzenthaler",
    "Arnulf Jentzen",
    "Xiaojie Wang"
  ],
  "comment": "39 pages",
  "categories": [
    "math.NA",
    "math.PR"
  ],
  "abstract": "Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonlinear stochastic differential equations. It turns out that well-known numerical approximation processes such as Euler-Maruyama approximations, linear-implicit Euler approximations, and some tamed Euler approximations from the literature rarely preserve exponential integrability properties of the exact solution. The main contribution of this article is to identify a class of stopped increment-tamed Euler approximations which preserve exponential integrability properties of the exact solution under minor additional assumptions on the involved functions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-06T21:10:54.000Z",
      "abstract": "Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonlinear stochastic differential equations. It turns out that well-known numerical approximation processes such as Euler-Maruyama approximations, linear-implicit Euler approximations and some tamed Euler approximations from the literature rarely preserve exponential integrability properties of the exact solution. The main contribution of this article is to identify a class of stopped increment-tamed Euler approximations which preserve exponential integrability properties of the exact solution under minor additional assumptions on the involved functions.",
      "comment": "32 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-11-20T02:37:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C30"
    ],
    "keywords": [
      "nonlinear stochastic differential equations",
      "numerical approximation processes",
      "preserve exponential integrability properties",
      "rarely preserve exponential integrability",
      "euler approximations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7657H"
    }
  }
}