{
  "id": "0710.3687",
  "version": "v1",
  "published": "2007-10-19T12:21:33.000Z",
  "updated": "2007-10-19T12:21:33.000Z",
  "title": "On invariant measures of stochastic recursions in a critical case",
  "authors": [
    "Dariusz Buraczewski"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/105051607000000140 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2007, Vol. 17, No. 4, 1245-1272",
  "doi": "10.1214/105051607000000140",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider an autoregressive model on $\\mathbb{R}$ defined by the recurrence equation $X_n=A_nX_{n-1}+B_n$, where $\\{(B_n,A_n)\\}$ are i.i.d. random variables valued in $\\mathbb{R}\\times\\mathbb{R}^+$ and $\\mathbb {E}[\\log A_1]=0$ (critical case). It was proved by Babillot, Bougerol and Elie that there exists a unique invariant Radon measure of the process $\\{X_n\\}$. The aim of the paper is to investigate its behavior at infinity. We describe also stationary measures of two other stochastic recursions, including one arising in queuing theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-19T12:21:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60B15",
      "60G50"
    ],
    "keywords": [
      "stochastic recursions",
      "critical case",
      "invariant measures",
      "unique invariant radon measure",
      "random variables"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.3687B"
    }
  }
}