{
  "id": "1310.4333",
  "version": "v3",
  "published": "2013-10-16T11:25:42.000Z",
  "updated": "2015-07-28T06:55:48.000Z",
  "title": "A criterion for invariant measures of Itô processes based on the symbol",
  "authors": [
    "Anita Behme",
    "Alexander Schnurr"
  ],
  "comment": "Published at http://dx.doi.org/10.3150/14-BEJ618 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)",
  "journal": "Bernoulli 2015, Vol. 21, No. 3, 1697-1718",
  "doi": "10.3150/14-BEJ618",
  "categories": [
    "math.PR"
  ],
  "abstract": "An integral criterion for the existence of an invariant measure of an It\\^{o} process is developed. This new criterion is based on the probabilistic symbol of the It\\^{o} process. In contrast to the standard integral criterion for invariant measures of Markov processes based on the generator, no test functions and hence no information on the domain of the generator is needed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-06T07:48:25.000Z",
      "title": "A Criterion for Invariant Measures of Itô Processes based on the Symbol",
      "abstract": "An integral criterion for the existence of an invariant measure of an It\\^o process is developed. This new criterion is based on the probabilistic symbol of the It\\^o process. In contrast to the standard integral criterion for invariant measures of Markov processes based on the generator, no test functions and hence no information on the domain of the generator is needed.",
      "comment": "21 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-07-28T06:55:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G10",
      "60G51",
      "60J35",
      "47G30"
    ],
    "keywords": [
      "invariant measure",
      "standard integral criterion",
      "probabilistic symbol",
      "test functions",
      "markov processes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4333B"
    }
  }
}