{
  "id": "1609.06080",
  "version": "v1",
  "published": "2016-09-20T10:14:12.000Z",
  "updated": "2016-09-20T10:14:12.000Z",
  "title": "Convergence Rate of Euler-Maruyama Scheme for SDEs with Rough Coefficients",
  "authors": [
    "Jianhai Bao",
    "Xing Huang",
    "Chenggui Yuan"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we are concerned with convergence rate of Euler-Maruyama scheme for stochastic differential equations with rough coefficients. The key contributions lie in (i), by means of regularity of non-degenerate Kolmogrov equation, we investigate convergence rate of Euler-Maruyama scheme for a class of stochastic differential equations, which allow the drifts to be Dini-continuous and unbounded; (ii) by the aid of regularization properties of degenerate Kolmogrov equation, we discuss convergence rate of Euler-Maruyama scheme for a range of degenerate stochastic differential equations, where the drift is locally H\\\"older-Dini continuous of order $\\frac{2}{3}$ with respect to the first component, and is merely Dini-continuous concerning the second component.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-20T10:14:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H35",
      "41A25",
      "60H10",
      "60C30"
    ],
    "keywords": [
      "convergence rate",
      "euler-maruyama scheme",
      "rough coefficients",
      "degenerate stochastic differential equations",
      "non-degenerate kolmogrov equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}