{
  "id": "math/0512386",
  "version": "v1",
  "published": "2005-12-16T15:07:29.000Z",
  "updated": "2005-12-16T15:07:29.000Z",
  "title": "Relative entropy and waiting times for continuous-time Markov processes",
  "authors": [
    "Jean-Rene Chazottes",
    "Cristian Giardina",
    "Frank Redig"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one does need a reference measure and so the natural object is relative entropy rather than entropy. In this paper we elaborate on this in the case of continuous-time Markov processes with finite state space. A reference measure of special interest is the one associated to the time-reversed process. In that case relative entropy is interpreted as the entropy production rate. The main results of this paper are: almost-sure convergence to relative entropy of suitable waiting-times and their fluctuation properties (central limit theorem and large deviation principle).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-16T15:07:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous-time markov processes",
      "relative entropy",
      "waiting times",
      "reference measure",
      "large deviation principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12386C"
    }
  }
}