{
  "id": "math/0509317",
  "version": "v2",
  "published": "2005-09-14T15:19:41.000Z",
  "updated": "2006-09-25T09:26:05.000Z",
  "title": "Stationary processes whose filtrations are standard",
  "authors": [
    "X. Bressaud",
    "A. Maass",
    "S. Martinez",
    "J. San Martin"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117906000000151 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2006, Vol. 34, No. 4, 1589-1600",
  "doi": "10.1214/009117906000000151",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We study the standard property of the natural filtration associated to a 0--1 valued stationary process. In our main result we show that if the process has summable memory decay, then the associated filtration is standard. We prove it by coupling techniques. For a process whose associated filtration is standard, we construct a product type filtration extending it, based upon the usual couplings and the Vershik's criterion for standardness.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-09-25T09:26:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60A10",
      "60G10"
    ],
    "keywords": [
      "stationary processes",
      "associated filtration",
      "natural filtration",
      "product type filtration extending",
      "summable memory decay"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9317B"
    }
  }
}