{
  "id": "2104.03468",
  "version": "v1",
  "published": "2021-04-08T01:50:38.000Z",
  "updated": "2021-04-08T01:50:38.000Z",
  "title": "Projection scheme for polynomial diffusions on the unit ball",
  "authors": [
    "Takuya Nakagawa",
    "Dai Taguchi",
    "Tomooki Yuasa"
  ],
  "comment": "18 pages, 10 figures",
  "categories": [
    "math.PR",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "In this article, we consider numerical schemes for polynomial diffusions on the unit ball $\\mathscr{B}^{d}$, which are solutions of stochastic differential equations with a diffusion coefficient of the form $\\sqrt{1-|x|^{2}}$. We introduce a projection scheme on the unit ball $\\mathscr{B}^{d}$ based on a backward Euler--Maruyama scheme and provide the $L^{2}$-rate of convergence. The main idea to consider the numerical scheme is the transformation argument introduced by Swart [29] for proving the pathwise uniqueness for some stochastic differential equation with a non-Lipschitz diffusion coefficient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-08T01:50:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C30",
      "60H35",
      "91G60"
    ],
    "keywords": [
      "unit ball",
      "polynomial diffusions",
      "projection scheme",
      "stochastic differential equation",
      "non-lipschitz diffusion coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}