{
  "id": "1210.7193",
  "version": "v2",
  "published": "2012-10-26T16:57:54.000Z",
  "updated": "2014-02-17T12:59:11.000Z",
  "title": "On the notion(s) of duality for Markov processes",
  "authors": [
    "Sabine Jansen",
    "Noemi Kurt"
  ],
  "comment": "52 pages, 3 tables, 3 figures, revised version",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We provide a systematic study of the notion of duality of Markov processes with respect to a function. We discuss the relation of this notion with duality with respect to a measure as studied in Markov process theory and potential theory and give functional analytic results including existence and uniqueness criteria and a comparison of the spectra of dual semi-groups. The analytic framework builds on the notion of dual pairs, convex geometry, and Hilbert spaces. In addition, we formalize the notion of pathwise duality as it appears in population genetics and interacting particle systems. We discuss the relation of duality with rescalings, stochastic monotonicity, intertwining, symmetries, and quantum many-body theory, reviewing known results and establishing some new connections.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-17T12:59:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "46N30",
      "47D07",
      "60J05"
    ],
    "keywords": [
      "markov processes",
      "quantum many-body theory",
      "markov process theory",
      "functional analytic results",
      "analytic framework builds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7193J"
    }
  }
}