{
  "id": "2303.05945",
  "version": "v2",
  "published": "2023-03-10T14:26:53.000Z",
  "updated": "2023-03-21T13:46:31.000Z",
  "title": "Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift",
  "authors": [
    "Paweł Przybyłowicz",
    "Verena Schwarz",
    "Michaela Szölgyenyi"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted approximation schemes and provide lower error bounds of order $3/4$ for both classes of approximation schemes. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-03-21T13:46:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C30",
      "65C20",
      "60H10",
      "68Q25"
    ],
    "keywords": [
      "jump-diffusion sdes",
      "discontinuous drift",
      "optimality",
      "jump-diffusion stochastic differential equations",
      "sharp lower error bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}