{
  "id": "1105.0478",
  "version": "v3",
  "published": "2011-05-03T05:37:56.000Z",
  "updated": "2012-04-08T16:21:43.000Z",
  "title": "On $L_1$-Weak Ergodicity of nonhomogeneous discrete Markov processes and its applications",
  "authors": [
    "Farrukh Mukhamedov"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR",
    "math.DS"
  ],
  "abstract": "In the present paper we investigate the $L_1$-weak ergodicity of nonhomogeneous discrete Markov processes with general state spaces. Note that the $L_1$-weak ergodicity is weaker than well-known weak ergodicity. We provide a necessary and sufficient condition for such processes to satisfy the $L_1$-weak ergodicity. Moreover, we apply the obtained results to establish $L_1$-weak ergodicity of discrete time quadratic stochastic processes. As an application of the main result, certain concrete examples are also provided.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-04-08T16:21:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "15A51"
    ],
    "keywords": [
      "nonhomogeneous discrete markov processes",
      "application",
      "discrete time quadratic stochastic processes",
      "general state spaces",
      "well-known weak ergodicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.0478M"
    }
  }
}