{
  "id": "1403.2522",
  "version": "v1",
  "published": "2014-03-11T10:05:52.000Z",
  "updated": "2014-03-11T10:05:52.000Z",
  "title": "Fluid approach to two-sided Markov-modulated Brownian motion",
  "authors": [
    "Guy Latouche",
    "Giang T. Nguyen"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We extend to Markov-modulated Brownian motion (MMBM) the renewal approach which has been successfully applied to the analysis of Markov-modulated fluid models. It has recently been shown that MMBM may be expressed as the limit of a parameterized family of Markov-modulated fluid models. We prove that the weak convergence also holds for systems with two reflecting boundaries, one at zero and one at $b >0$, and that the stationary distributions of the approximating fluid models converge to the stationary distribution of the two-sided reflected MMBM. Thus, we obtain a new representation for the stationary distribution, effectively separating the limiting behaviour of the process at the boundaries from its behaviour in the interior of $(0,b)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-11T10:05:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-sided markov-modulated brownian motion",
      "fluid approach",
      "stationary distribution",
      "markov-modulated fluid models",
      "approximating fluid models converge"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.2522L"
    }
  }
}