{
  "id": "1108.4086",
  "version": "v1",
  "published": "2011-08-20T03:45:18.000Z",
  "updated": "2011-08-20T03:45:18.000Z",
  "title": "On optimal stationary couplings between stationary processes",
  "authors": [
    "Ludger Rueschendorf",
    "Tomonari Sei"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "By a classical result of Gray, Neuhoff and Shields (1975) the $\\bar\\varrho$ distance between stationary processes is identified with an optimal stationary coupling problem of the corresponding stationary measures on the infinite product spaces. This is a modification of the optimal coupling problem from Monge--Kantorovich theory. In this paper we derive some general classes of examples of optimal stationary couplings which allow to calculate the $\\bar\\varrho$ distance in these cases in explicit form. We also extend the $\\bar\\varrho$ distance to random fields and to general nonmetric distance functions and give a construction method for optimal stationary $\\bar c$-couplings. Our assumptions need in this case a geometric positive curvature condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-20T03:45:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60G10"
    ],
    "keywords": [
      "stationary processes",
      "general nonmetric distance functions",
      "optimal stationary coupling problem",
      "geometric positive curvature condition",
      "infinite product spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4086R"
    }
  }
}