{
  "id": "2306.12116",
  "version": "v1",
  "published": "2023-06-21T09:01:08.000Z",
  "updated": "2023-06-21T09:01:08.000Z",
  "title": "Mean square exponential stability of numerical methods for stochastic differential delay equations",
  "authors": [
    "Guangqiang Lan",
    "Qi Liu"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NA",
    "cs.NA",
    "math.PR"
  ],
  "abstract": "Mean square exponential stability of $\\theta$-EM and modified truncated Euler-Maruyama (MTEM) methods for stochastic differential delay equations (SDDEs) are investigated in this paper. We present new criterion of mean square exponential stability of the $\\theta$-EM and MTEM methods for SDDEs, which are different from most existing results under Khasminskii-type conditions. Two examples are provided to support our conclusions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-21T09:01:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C30",
      "65C20",
      "65L05",
      "65L20"
    ],
    "keywords": [
      "mean square exponential stability",
      "stochastic differential delay equations",
      "numerical methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}