{
  "id": "2012.13656",
  "version": "v1",
  "published": "2020-12-26T00:52:07.000Z",
  "updated": "2020-12-26T00:52:07.000Z",
  "title": "Distribution Dependent Stochastic Differential Equations",
  "authors": [
    "Xing Huang",
    "Panpan Ren",
    "Feng-Yu Wang"
  ],
  "comment": "44 pages. arXiv admin note: text overlap with arXiv:2002.08652, arXiv:2010.08950",
  "categories": [
    "math.PR"
  ],
  "abstract": "Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs for short) have been intensively investigated. In this paper we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-26T00:52:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B05",
      "60B10"
    ],
    "keywords": [
      "distribution dependent stochastic differential equations",
      "nonlinear fokker-planck equations",
      "long time large deviations",
      "weak solutions",
      "regularity estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}