{
  "id": "1702.03917",
  "version": "v1",
  "published": "2017-02-13T18:46:38.000Z",
  "updated": "2017-02-13T18:46:38.000Z",
  "title": "MEXIT: Maximal un-coupling times for Markov processes",
  "authors": [
    "P. A. Ernst",
    "W. S. Kendall",
    "G. O. Roberts",
    "J. S. Rosenthal"
  ],
  "comment": "23 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "Classical coupling constructions arrange for copies of the \\emph{same} Markov process started at two \\emph{different} initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two \\emph{different} Markov processes to remain equal for as long as possible, when started in the \\emph{same} state. We refer to this \"un-coupling\" or \"maximal agreement\" construction as \\emph{MEXIT}, standing for \"maximal exit\" time. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for Markov chains in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-13T18:46:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60G05"
    ],
    "keywords": [
      "markov process",
      "maximal un-coupling times",
      "explicit mexit construction",
      "probabilistic settings",
      "initial states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}