{
  "id": "1401.6400",
  "version": "v2",
  "published": "2014-01-24T16:58:12.000Z",
  "updated": "2015-02-02T16:37:05.000Z",
  "title": "The stationary distribution of a Markov jump process glued together from two state spaces at two vertices",
  "authors": [
    "Bence Mélykúti",
    "Peter Pfaffelhuber"
  ],
  "comment": "28 pages. Proposition 4, Theorem 7 and their proofs have been changed to correct errors. The notation has been modified. This is a revision of our Author's Original Manuscript submitted for publication to Stochastic Models, Taylor & Francis LLC",
  "categories": [
    "math.PR"
  ],
  "abstract": "We compute the stationary distribution of a continuous-time Markov chain which is constructed by gluing together two finite, irreducible Markov chains by identifying a pair of states of one chain with a pair of states of the other and keeping all transition rates from either chain (the rates between the two shared states are summed). The result expresses the stationary distribution of the glued chain in terms of quantities of the two original chains. Some of the required terms are nonstandard but can be computed by solving systems of linear equations using the transition rate matrices of the two original chains. Special emphasis is given to the cases when the stationary distribution of the glued chain is a multiple of the equilibria of the original chains, and when not, for which bounds are derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-24T16:58:12.000Z",
      "title": "The stationary distribution of a Markov jump process on a state space glued together from two state spaces at two vertices",
      "abstract": "We compute the stationary distribution of a continuous-time Markov chain on a finite state space which is constructed by gluing together two irreducible, continuous-time Markov chains by identifying a pair of states of one chain with a pair of states of the other chain and keeping all transition rates from either chain (the rates between the two shared states are summed). The result expresses the stationary distribution of the glued chain in terms of quantities of the two original chains. Some of the required terms are nonstandard but can be computed by solving systems of linear equations using the transition rate matrices of the two original chains. Special emphasis is given to the difference between the parallel case, when the stationary distribution of the glued chain is a multiple of the equilibria of the original chains, and the non-parallel case, for which bounds are derived.",
      "comment": "24 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-02T16:37:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "60K15"
    ],
    "keywords": [
      "stationary distribution",
      "markov jump process",
      "state space",
      "continuous-time markov chain",
      "original chains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.6400M"
    }
  }
}