{
  "id": "2212.00411",
  "version": "v1",
  "published": "2022-12-01T10:28:04.000Z",
  "updated": "2022-12-01T10:28:04.000Z",
  "title": "Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs",
  "authors": [
    "Paweł Przybyłowicz",
    "Verena Schwarz",
    "Michaela Szölgyenyi"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We investigate the error of the randomized Milstein algorithm for solving scalar jump-diffusion stochastic differential equations. We provide a complete error analysis under substantially weaker assumptions than known in the literature. In case the jump-commutativity condition is satisfied, we prove optimality of the randomized Milstein algorithm by proving a matching lower bound. Moreover, we give some insight into the multidimensional case by investigating the optimal convergence rate for the approximation of jump-diffusion type L\\'evys' areas. Finally, we report numerical experiments that support our theoretical findings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-01T10:28:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68Q25",
      "65C30",
      "60H10"
    ],
    "keywords": [
      "randomized milstein algorithm",
      "jump-diffusion sdes",
      "scalar jump-diffusion stochastic differential equations",
      "approximation",
      "solving scalar jump-diffusion stochastic differential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}