{
  "id": "0706.4193",
  "version": "v1",
  "published": "2007-06-28T10:50:35.000Z",
  "updated": "2007-06-28T10:50:35.000Z",
  "title": "Transportation-information inequalities for Markov processes",
  "authors": [
    "Arnaud Guillin",
    "Christian Leonard",
    "Liming Wu",
    "Nian Yao"
  ],
  "journal": "Probability Theory and Related Fields 144, 3-4 (2009) 669-695",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "In this paper, one investigates the following type of transportation-information $T_cI$ inequalities: $\\alpha(T_c(\\nu,\\mu))\\le I(\\nu|\\mu)$ for all probability measures $\\nu$ on some metric space $(\\XX, d)$, where $\\mu$ is a given probability measure, $T_c(\\nu,\\mu)$ is the transportation cost from $\\nu$ to $\\mu$ with respect to some cost function $c(x,y)$ on $\\XX^2$, $I(\\nu|\\mu)$ is the Fisher-Donsker-Varadhan information of $\\nu$ with respect to $\\mu$ and $\\alpha: [0,\\infty)\\to [0,\\infty]$ is some left continuous increasing function. Using large deviation techniques, it is shown that $T_cI$ is equivalent to some concentration inequality for the occupation measure of a $\\mu$-reversible ergodic Markov process related to $I(\\cdot|\\mu)$, a counterpart of the characterizations of transportation-entropy inequalities, recently obtained by Gozlan and L\\'eonard in the i.i.d. case . Tensorization properties of $T_cI$ are also derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-28T10:50:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "markov processes",
      "transportation-information inequalities",
      "inequality",
      "ergodic markov process",
      "probability measure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.4193G"
    }
  }
}