{
  "id": "1812.04583",
  "version": "v1",
  "published": "2018-12-11T18:10:27.000Z",
  "updated": "2018-12-11T18:10:27.000Z",
  "title": "On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift",
  "authors": [
    "Konstantinos Dareiotis",
    "Máté Gerencsér"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of $\\alpha$-H\\\"older drift in recent literature the rate $\\alpha/2$ was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to $1/2$ for all $\\alpha>0$. The result extends to Dini continuous coefficients, while in $d=1$ also to a class of everywhere discontinuous coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-11T18:10:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H35",
      "60H10",
      "65C30"
    ],
    "keywords": [
      "euler-maruyama scheme",
      "regularisation",
      "irregular drift coefficients",
      "nondegenerate sdes",
      "strong rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}