{
  "id": "2309.11396",
  "version": "v1",
  "published": "2023-09-20T15:23:12.000Z",
  "updated": "2023-09-20T15:23:12.000Z",
  "title": "Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space",
  "authors": [
    "Luis Mario Chaparro Jáquez",
    "Elena Issoglio",
    "Jan Palczewski"
  ],
  "comment": "20 pages, 3 figures",
  "categories": [
    "math.PR",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function, in particular belonging to the Holder-Zygmund space $C^{-\\gamma}$ of negative order $-\\gamma<0$ in the spacial variable. We design an Euler-Maruyama numerical scheme and prove its convergence, obtaining an upper bound for the strong $L^1$ convergence rate. We finally implement the scheme and discuss the results obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-20T15:23:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C30",
      "60H35",
      "65C20",
      "46F99"
    ],
    "keywords": [
      "convergence rate",
      "besov space",
      "distributional drift",
      "upper bound",
      "euler-maruyama numerical scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}