{
  "id": "1708.07857",
  "version": "v1",
  "published": "2017-08-25T18:40:55.000Z",
  "updated": "2017-08-25T18:40:55.000Z",
  "title": "A note on pathwise stability and positivity of nonlinear stochastic differential equations",
  "authors": [
    "Ioannis S. Stamatiou"
  ],
  "comment": "8 pages, 3 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "We use the semi-discrete method, originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics, 89(6), to reproduce qualitative properties of a class of nonlinear stochastic differential equations with nonnegative, non-globally Lipschitz coefficients and a unique equilibrium solution. The proposed fixed-time step method preserves the positivity of solutions and reproduces the almost sure asymptotic stability behavior of the equilibrium with no time-step restrictions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-25T18:40:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H35",
      "65C20",
      "65C30",
      "65J15",
      "65L20"
    ],
    "keywords": [
      "nonlinear stochastic differential equations",
      "pathwise stability",
      "positivity",
      "sure asymptotic stability behavior",
      "fixed-time step method preserves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}