{
  "id": "2308.04075",
  "version": "v1",
  "published": "2023-08-08T06:21:07.000Z",
  "updated": "2023-08-08T06:21:07.000Z",
  "title": "Boundary-preserving Lamperti-splitting scheme for some Stochastic Differential Equations",
  "authors": [
    "Johan Ulander"
  ],
  "comment": "17 pages, 3 figures",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We propose and analyse an explicit boundary-preserving scheme for the strong approximations of some SDEs with non-globally Lipschitz drift and diffusion coefficients whose state-space is bounded. The scheme consists of a Lamperti transform followed by a Lie--Trotter splitting. We prove $L^{p}(\\Omega)$-convergence of order $1$, for every $p \\in \\mathbb{N}$, of the scheme and exploit the Lamperti transform to confine the numerical approximations to the state-space of the considered SDE. We provide numerical experiments that confirm the theoretical results and compare the proposed Lamperti-splitting scheme to other numerical schemes for SDEs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-08T06:21:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H35",
      "65C30"
    ],
    "keywords": [
      "stochastic differential equations",
      "boundary-preserving lamperti-splitting scheme",
      "lamperti transform",
      "non-globally lipschitz drift",
      "diffusion coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}