{
  "id": "1209.3533",
  "version": "v1",
  "published": "2012-09-17T00:50:17.000Z",
  "updated": "2012-09-17T00:50:17.000Z",
  "title": "Generalized inverses of Markovian kernels in terms of properties of the Markov chain",
  "authors": [
    "Jeffrey J. Hunter"
  ],
  "comment": "21 pages",
  "doi": "10.1016/j.laa.2013.08.037",
  "categories": [
    "math.PR"
  ],
  "abstract": "All one-condition generalized inverses of the Markovian kernel I - P, where P is the transition matrix of a finite irreducible Markov chain, can be uniquely specified in terms of the stationary probabilities and the mean first passage times of the underlying Markov chain. Special sub-families include the group inverse of I - P, Kemeny and Snell's fundamental matrix of the Markov chain and the Moore-Penrose g-inverse. The elements of some sub-families of the generalized inverses can also be re-expressed involving the second moments of the recurrence time variables. Some applications to Kemeny's constant and perturbations of Markov chains are also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-17T00:50:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A09",
      "15B51",
      "60J10"
    ],
    "keywords": [
      "markovian kernel",
      "mean first passage times",
      "properties",
      "finite irreducible markov chain",
      "recurrence time variables"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.3533H"
    }
  }
}