{
  "id": "1912.06121",
  "version": "v1",
  "published": "2019-12-12T18:39:38.000Z",
  "updated": "2019-12-12T18:39:38.000Z",
  "title": "Asymptotic strong Feller property and local weak irreducibility via generalized couplings",
  "authors": [
    "Oleg Butkovsky",
    "Fabrice Wunderlich"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this short note we show how the asymptotic strong Feller property (ASF) and local weak irreducibility can be established via generalized couplings. We also prove that a stronger form of ASF together with local weak irreducibility implies uniqueness of an invariant measure. The latter result is optimal in a certain sense and complements some of the corresponding results of Hairer, Mattingly (2008).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-12T18:39:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic strong feller property",
      "generalized couplings",
      "local weak irreducibility implies uniqueness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}