{
  "id": "1905.07883",
  "version": "v1",
  "published": "2019-05-20T05:36:27.000Z",
  "updated": "2019-05-20T05:36:27.000Z",
  "title": "Stability for Stochastic McKean-Vlasov Equations with Non-Lipschitz Coefficients",
  "authors": [
    "Xiaojie Ding",
    "Huijie Qiao"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we consider the stability of a type of stochastic McKean-Vlasov equations with non-Lipschitz coefficients. Firstly, sufficient conditions are given for the exponential stability of the second moments for their solutions in terms of a Lyapunov function. Then we weaken the conditions and furthermore obtain exponentially 2-ultimate boundedness of their solutions. Finally, almost surely asymptotic stability of their solutions is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-20T05:36:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15"
    ],
    "keywords": [
      "stochastic mckean-vlasov equations",
      "non-lipschitz coefficients",
      "lyapunov function",
      "sufficient conditions",
      "surely asymptotic stability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}