{
  "id": "math/0606668",
  "version": "v3",
  "published": "2006-06-27T08:06:34.000Z",
  "updated": "2007-10-30T13:07:42.000Z",
  "title": "A central limit theorem for stochastic recursive sequences of topical operators",
  "authors": [
    "Glenn Merlet"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/105051607000000168 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "The Annals of Applied Probability 17, 4 (2007) 1347-1361",
  "doi": "10.1214/105051607000000168",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "Let $(A_n)_{n\\in\\mathbb{N}}$ be a stationary sequence of topical (i.e., isotone and additively homogeneous) operators. Let $x(n,x_0)$ be defined by $x(0,x_0)=x_0$ and $x(n+1,x_0)=A_nx(n,x_0)$. It can model a wide range of systems including train or queuing networks, job-shop, timed digital circuits or parallel processing systems. When $(A_n)_{n\\in\\mathbb{N}}$ has the memory loss property, $(x(n,x_0))_{n\\in\\mathbb{N}}$ satisfies a strong law of large numbers. We show that it also satisfies the CLT if $(A_n)_{n\\in \\mathbb{N}}$ fulfills the same mixing and integrability assumptions that ensure the CLT for a sum of real variables in the results by P. Billingsley and I. Ibragimov.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-10-30T13:07:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93C65",
      "60F05",
      "93B25",
      "60J10"
    ],
    "keywords": [
      "central limit theorem",
      "stochastic recursive sequences",
      "topical operators",
      "memory loss property",
      "stationary sequence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6668M"
    }
  }
}