{
  "id": "2108.05802",
  "version": "v1",
  "published": "2021-08-12T15:30:34.000Z",
  "updated": "2021-08-12T15:30:34.000Z",
  "title": "Invariant Probability Measure for McKean-Vlasov SDEs with Singular Drifts",
  "authors": [
    "Xing Huang",
    "Shen Wang",
    "Fen-Fen Yang"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, utilizing Wang's Harnack inequality with power and the Banach fixed point theorem, the weak well-posedness for distribution dependent SDEs with integrable drift is investigated. In addition, using a trick of decoupled method, some regularity such as relative entropy and Sobolev's estimate of invariant probability measure are proved. Furthermore, by comparing two stationary Fokker-Planck-Kolmogorov equations, the existence and uniqueness of invariant probability measure for McKean-Vlasov SDEs are obtained by log-Sobolev's inequality and Banach's fixed theorem. Finally, some examples are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-12T15:30:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariant probability measure",
      "mckean-vlasov sdes",
      "singular drifts",
      "stationary fokker-planck-kolmogorov equations",
      "banach fixed point theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}