{
  "id": "2107.11076",
  "version": "v1",
  "published": "2021-07-23T08:37:11.000Z",
  "updated": "2021-07-23T08:37:11.000Z",
  "title": "A monotone scheme for nonlinear partial integro-differential equations with the convergence rate of $α$-stable limit theorem under sublinear expectation",
  "authors": [
    "Mingshang Hu",
    "Lianzi Jiang",
    "Gechun Liang"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "In this paper, we propose a monotone approximation scheme for a class of fully nonlinear partial integro-differential equations (PIDEs) which characterize the nonlinear $\\alpha$-stable L\\'{e}vy processes under sublinear expectation space with $\\alpha \\in(1,2)$. Two main results are obtained: (i) the error bounds for the monotone approximation scheme of nonlinear PIDEs, and (ii) the convergence rates of a generalized central limit theorem of Bayraktar-Munk for $\\alpha$-stable random variables under sublinear expectation. Our proofs use and extend techniques introduced by Krylov and Barles-Jakobsen.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-23T08:37:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "45K05",
      "60F05",
      "60H30",
      "60G51",
      "65M15"
    ],
    "keywords": [
      "nonlinear partial integro-differential equations",
      "sublinear expectation",
      "stable limit theorem",
      "convergence rate",
      "monotone scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}