{
  "id": "1308.4967",
  "version": "v1",
  "published": "2013-08-22T19:46:04.000Z",
  "updated": "2013-08-22T19:46:04.000Z",
  "title": "The asymptotic strong Feller property does not imply the e-property for Markov-Feller semigroups",
  "authors": [
    "Joanna Jaroszewska"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "T. Szarek [Stud. Math. 189 (2008), {\\S} 4] have discussed the relationship between two important notions concerning Markov semigroups: the asymptotic strong Feller property and the e-property, asserting that the former property implies the latter one. In this very short note we rectify this issue exhibiting a simple example of a Markov-Feller semigroup enjoying the asymptotic strong Feller property, for which the e-property is not satisfied. (See also the comment on a connection between the asymptotic strong Feller property and the e-property by T. Szarek, D. Worm [ETDS 32 (2012), {\\S} 1]). Additionally we give a very simple example - in comparing with the one given by T. Szarek [Stud. Math. 189 (2008), {\\S} 4] - showing that also the converse implication does not hold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-22T19:46:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "60J25"
    ],
    "keywords": [
      "asymptotic strong feller property",
      "markov-feller semigroup",
      "e-property",
      "important notions concerning markov semigroups",
      "simple example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.4967J"
    }
  }
}