{
  "id": "1210.2004",
  "version": "v3",
  "published": "2012-10-06T21:59:42.000Z",
  "updated": "2015-01-15T22:05:50.000Z",
  "title": "Large deviations of the empirical flow for continuous time Markov chains",
  "authors": [
    "Lorenzo Bertini",
    "Alessandra Faggionato",
    "Davide Gabrielli"
  ],
  "comment": "Minor revision, to appear on Annales de l'Institut Henri Poincare (B) Probability and Statistics",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a continuous time Markov chain on a countable state space and prove a joint large deviation principle for the empirical measure and the empirical flow, which accounts for the total number of jumps between pairs of states. We give a direct proof using tilting and an indirect one by contraction from the empirical process.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-31T15:12:47.000Z",
      "abstract": "We consider a continuous time Markov chain on a countable (finite or infinite) state space and prove a joint large deviation principle for the empirical measure and the empirical flow, which accounts for the total number of jumps between pairs of states. We give a direct proof using tilting and an undirected one by contraction from the empirical process. By projection, we recover the Donsker--Varadhan large deviation principle for the empirical measure.",
      "comment": "41 pages, no figures. Corrected version. Old Proposition 2.7 and related proof corrected and moved to a companion paper",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-01-15T22:05:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60J27",
      "82C05"
    ],
    "keywords": [
      "continuous time markov chain",
      "empirical flow",
      "donsker-varadhan large deviation principle",
      "joint large deviation principle",
      "empirical measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.2004B"
    }
  }
}