{
  "id": "2010.14178",
  "version": "v1",
  "published": "2020-10-27T10:23:51.000Z",
  "updated": "2020-10-27T10:23:51.000Z",
  "title": "Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels",
  "authors": [
    "Max Fathi",
    "Dan Mikulincer"
  ],
  "comment": "29 pages, comments are welcome",
  "categories": [
    "math.PR",
    "math.AP",
    "math.FA"
  ],
  "abstract": "We investigate stability of invariant measures of diffusion processes with respect to $L^p$ distances on the coefficients, under an assumption of log-concavity. The method is a variant of a technique introduced by Crippa and De Lellis to study transport equations. As an application, we prove a partial extension of an inequality of Ledoux, Nourdin and Peccati relating transport distances and Stein discrepancies to a non-Gaussian setting via the moment map construction of Stein kernels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-27T10:23:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariant measures",
      "diffusion processes",
      "stein kernels",
      "stability estimates",
      "moment measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}