{
  "id": "1809.01742",
  "version": "v1",
  "published": "2018-09-05T21:40:32.000Z",
  "updated": "2018-09-05T21:40:32.000Z",
  "title": "On the wellposedness of some McKean models with moderated or singular diffusion coefficient",
  "authors": [
    "Mireille Bossy",
    "Jean Francois Jabir"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate the well-posedness problem related to two models of nonlinear McKean Stochastic Differential Equations with some local interaction in the diffusion term. First, we revisit the case of the McKean-Vlasov dynamics with moderate interaction, previously studied by Meleard and Jourdain in [16], under slightly weaker assumptions, by showing the existence and uniqueness of a weak solution using a Sobolev regularity framework instead of a Holder one. Second, we study the construction of a Lagrangian Stochastic model endowed with a conditional McKean diffusion term in the velocity dynamics and a nondegenerate diffusion term in the position dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-05T21:40:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular diffusion coefficient",
      "mckean models",
      "nonlinear mckean stochastic differential equations",
      "wellposedness",
      "conditional mckean diffusion term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}