{
  "id": "2106.12080",
  "version": "v1",
  "published": "2021-06-22T22:11:13.000Z",
  "updated": "2021-06-22T22:11:13.000Z",
  "title": "The stability and path-independence of additive functionals for multivalued McKean-Vlasov SDEs with non-Lipschitz coefficients",
  "authors": [
    "Jun Gong",
    "Huijie Qiao"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The work concerns the stability and path-independence of additive functionals for a type of multivalued McKean-Vlasov stochastic differential equations with non-Lipschitz coefficients. First, we prove the existence and uniqueness of strong solutions for multivalued McKean-Vlasov stochastic differential equation with non-Lipschitz coefficients. And then, the exponential stability of second moments for their solutions in terms of a Lyapunov function is shown. Next, we weaken the conditions and furthermore obtain the exponentially 2-ultimate boundedness of their solutions. Finally, the path-independence of additive functionals for their solutions is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-22T22:11:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10"
    ],
    "keywords": [
      "non-lipschitz coefficients",
      "multivalued mckean-vlasov sdes",
      "additive functionals",
      "multivalued mckean-vlasov stochastic differential equation",
      "path-independence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}