{
  "id": "1809.08423",
  "version": "v1",
  "published": "2018-09-22T10:17:58.000Z",
  "updated": "2018-09-22T10:17:58.000Z",
  "title": "On the performance of the Euler-Maruyama scheme for SDEs with discontinuous drift coefficient",
  "authors": [
    "Thomas Müller-Gronbach",
    "Larisa Yaroslavtseva"
  ],
  "categories": [
    "math.NA",
    "math.PR"
  ],
  "abstract": "Recently a lot of effort has been invested to analyze the $L_p$-error of the Euler-Maruyama scheme in the case of stochastic differential equations (SDEs) with a drift coefficient that may have discontinuities in space. For scalar SDEs with a piecewise Lipschitz drift coefficient and a Lipschitz diffusion coefficient that is non-zero at the discontinuity points of the drift coefficient so far only an $L_p$-error rate of at least $1/(2p)-$ has been proven. In the present paper we show that under the latter conditions on the coefficients of the SDE the Euler-Maruyama scheme in fact achieves an $L_p$-error rate of at least $1/2$ for all $p\\in [1,\\infty)$ as in the case of SDEs with Lipschitz coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-22T10:17:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C30",
      "65C20",
      "60H10"
    ],
    "keywords": [
      "euler-maruyama scheme",
      "discontinuous drift coefficient",
      "performance",
      "error rate",
      "stochastic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}