{
  "id": "1407.1486",
  "version": "v2",
  "published": "2014-07-06T11:35:53.000Z",
  "updated": "2014-09-17T05:22:38.000Z",
  "title": "Polynomial and exponential stability of $θ$-EM approximations to a class of stochastic differential equations",
  "authors": [
    "Yunjiao Hu",
    "Guangqiang Lan",
    "Chong Zhang"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "Both the mean square polynomial stability and exponential stability of $\\theta$ Euler-Maruyama approximation solutions of stochastic differential equations will be investigated for each $0\\le\\theta\\le 1$ by using an auxiliary function $F$ (see the following definition (2.3)). Sufficient conditions are obtained to ensure the polynomial and exponential stability of the numerical approximations. The results in Liu et al [12] will be improved and generalized to more general cases. Several examples and non stability results are presented to support our conclusions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-06T11:35:53.000Z",
      "abstract": "Both the mean square polynomial stability and exponential stability of $\\theta$ Euler-Maruyama approximation solutions of stochastic differential equations will be investigated for each $0\\le\\theta\\le 1$ by using an auxiliary function. Sufficient conditions are obtained to ensure the polynomial and exponential stability of the numerical solutions. Several examples and non stability results are presented to support our conclusions.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-17T05:22:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "65C30"
    ],
    "keywords": [
      "stochastic differential equations",
      "exponential stability",
      "em approximations",
      "mean square polynomial stability",
      "euler-maruyama approximation solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.1486H"
    }
  }
}