{
  "id": "1610.07047",
  "version": "v1",
  "published": "2016-10-22T13:33:25.000Z",
  "updated": "2016-10-22T13:33:25.000Z",
  "title": "Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient",
  "authors": [
    "Gunther Leobacher",
    "Michaela Szölgyenyi"
  ],
  "categories": [
    "math.NA",
    "math.PR"
  ],
  "abstract": "We prove strong convergence of order 1/5 of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler-Maruyama scheme and another numerical method, which is constructed by applying the Euler-Maruyama scheme to a transformation of the SDE we aim to solve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-22T13:33:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "65C30",
      "65C20",
      "65L20"
    ],
    "keywords": [
      "degenerate diffusion coefficient",
      "euler-maruyama method",
      "discontinuous drift",
      "multidimensional sdes",
      "euler-maruyama scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}