{
  "id": "0710.1520",
  "version": "v3",
  "published": "2007-10-08T11:52:27.000Z",
  "updated": "2009-02-09T07:53:07.000Z",
  "title": "Multicolor urn models with reducible replacement matrices",
  "authors": [
    "Arup Bose",
    "Amites Dasgupta",
    "Krishanu Maulik"
  ],
  "comment": "Published in at http://dx.doi.org/10.3150/08-BEJ150 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)",
  "journal": "Bernoulli 2009, Vol. 15, No. 1, 279-295",
  "doi": "10.3150/08-BEJ150",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider the multicolored urn model where, after every draw, balls of the different colors are added to the urn in a proportion determined by a given stochastic replacement matrix. We consider some special replacement matrices which are not irreducible. For three- and four-color urns, we derive the asymptotic behavior of linear combinations of the number of balls. In particular, we show that certain linear combinations of the balls of different colors have limiting distributions which are variance mixtures of normal distributions. We also obtain almost sure limits in certain cases in contrast to the corresponding irreducible cases, where only weak limits are known.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-02-09T07:53:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multicolor urn models",
      "reducible replacement matrices",
      "linear combinations",
      "special replacement matrices",
      "stochastic replacement matrix"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.1520B"
    }
  }
}