{
  "id": "1902.05712",
  "version": "v1",
  "published": "2019-02-15T07:51:53.000Z",
  "updated": "2019-02-15T07:51:53.000Z",
  "title": "On the Euler--Maruyama scheme for degenerate stochastic differential equations with non-sticky boundary condition",
  "authors": [
    "Dai Taguchi",
    "Akihiro Tanaka"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The aim of this paper is to study weak and strong convergence of the Euler--Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation $\\mathrm{d} X_t=\\sigma(X_t) \\mathrm{d} W_t$ with non-sticky boundary condition. For proving this, we first prove that the Euler--Maruyama scheme also satisfies non-sticky boundary condition. As an example, we consider stochastic differential equation $\\mathrm{d} X_t=|X_t|^{\\alpha} \\mathrm{d} W_t$, $\\alpha \\in (0,1/2)$ with non-sticky boundary condition and we give some remarks on CEV models in mathematical finance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-15T07:51:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C30",
      "60H35",
      "91G60"
    ],
    "keywords": [
      "euler-maruyama scheme",
      "one-dimensional degenerate stochastic differential equation",
      "satisfies non-sticky boundary condition",
      "strong convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}