{
  "id": "2501.16092",
  "version": "v2",
  "published": "2025-01-27T14:40:00.000Z",
  "updated": "2025-02-10T14:18:48.000Z",
  "title": "Log-Sobolev Inequality for Decoupled and McKean-Vlasov SDEs and Application on Exponential Ergodicity",
  "authors": [
    "Xing Huang",
    "Eva Kopfer",
    "Panpan Ren"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The exponential ergodicity in the \\( L^1 \\)-Wasserstein distance for partially dissipative McKean-Vlasov SDEs has been extensively studied. However, the question of exponential ergodicity in the \\( L^2 \\)-Wasserstein distance and relative entropy has remained unresolved. This paper addresses the problem by establishing the log-Sobolev inequality for both the time-marginal distributions and the invariant probability measure, providing a positive resolution. As part of the groundwork, the log-Sobolev inequality is investigated for the associated time-inhomogeneous semigroup. The main results are further extended to degenerate diffusion.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-02-10T14:18:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "log-sobolev inequality",
      "exponential ergodicity",
      "application",
      "invariant probability measure",
      "paper addresses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}