{
  "id": "1302.6647",
  "version": "v2",
  "published": "2013-02-27T02:23:48.000Z",
  "updated": "2015-06-19T08:00:43.000Z",
  "title": "On the large deviation rate function for the empirical measures of reversible jump Markov processes",
  "authors": [
    "Paul Dupuis",
    "Yufei Liu"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/13-AOP883 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2015, Vol. 43, No. 3, 1121-1156",
  "doi": "10.1214/13-AOP883",
  "categories": [
    "math.PR"
  ],
  "abstract": "The large deviations principle for the empirical measure for both continuous and discrete time Markov processes is well known. Various expressions are available for the rate function, but these expressions are usually as the solution to a variational problem, and in this sense not explicit. An interesting class of continuous time, reversible processes was identified in the original work of Donsker and Varadhan for which an explicit expression is possible. While this class includes many (reversible) processes of interest, it excludes the case of continuous time pure jump processes, such as a reversible finite state Markov chain. In this paper, we study the large deviations principle for the empirical measure of pure jump Markov processes and provide an explicit formula of the rate function under reversibility.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-27T02:23:48.000Z",
      "abstract": "The large deviations principle for the empirical measure for both continuous and discrete time Markov processes is well known. Various expressions are available for the rate function, but these expressions are usually as the solution to a variational problem, and in this sense not explicit. An interesting class of continuous time, reversible processes was identified in the original work of Donsker and Varadhan for which an explicit expression is possible. While this class includes many (reversible) processes of interest, it excludes the case of continuous time pure jump processes, such as a reversible finite state Markov chain. In this paper we study the large deviations principle for the empirical measure of pure jump Markov processes and provide an explicit formula of the rate function under reversibility.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-06-19T08:00:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation rate function",
      "reversible jump markov processes",
      "empirical measure",
      "time pure jump processes",
      "finite state markov chain"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.6647D"
    }
  }
}