{
  "id": "math/0009204",
  "version": "v3",
  "published": "2000-09-22T12:01:32.000Z",
  "updated": "2001-12-14T16:01:04.000Z",
  "title": "Processes with Long Memory: Regenerative Construction and Perfect Simulation",
  "authors": [
    "Francis Comets",
    "Roberto Fernandez",
    "Pablo A. Ferrari"
  ],
  "comment": "27 pages, one figure. Version accepted by Annals of Applied Probability. Small changes with respect to version 2",
  "journal": "Ann. Appl. Probab. Volume 12, Number 3 (2002), 921-943",
  "doi": "10.1214/aoap/1031863175",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence. Even though the process has infinite memory, its value at time 0 depends only on a finite, but random, number of these uniform variables. The algorithm is based on a recent regenerative construction of these measures by Ferrari, Maass, Mart{\\'\\i}nez and Ney. As applications, we discuss the perfect simulation of binary autoregressions and Markov chains on the unit interval.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2001-12-14T16:01:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68U20",
      "60K10",
      "62J02"
    ],
    "keywords": [
      "regenerative construction",
      "long memory",
      "perfect simulation algorithm",
      "unit interval",
      "stationary processes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9204C"
    }
  }
}