{
  "id": "2207.12108",
  "version": "v2",
  "published": "2022-07-25T12:19:13.000Z",
  "updated": "2022-10-15T15:57:09.000Z",
  "title": "Strong and weak convergence for averaging principle of DDSDE with singular drift",
  "authors": [
    "Mengyu Cheng",
    "Zimo Hao",
    "Michael Röckner"
  ],
  "comment": "41 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study the averaging principle for distribution dependent stochastic differential equations with drift in localized $L^p$ space. Using Zvonkin's transformation and estimates for solutions to Kolmogorov equations, we prove that the solutions of the original system strongly and weakly converge to the solution of the averaged system as the time scale $\\eps$ goes to zero. Moreover, we obtain rates of the strong and weak convergence that depend on $p$ respectively.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-10-15T15:57:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak convergence",
      "averaging principle",
      "singular drift",
      "distribution dependent stochastic differential equations",
      "zvonkins transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}