{
  "id": "1603.01945",
  "version": "v1",
  "published": "2016-03-07T05:51:07.000Z",
  "updated": "2016-03-07T05:51:07.000Z",
  "title": "Feedback control: two-sided Markov-modulated Brownian motion with instantaneous change of phase at boundaries",
  "authors": [
    "Guy Latouche",
    "Giang T. Nguyen"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a Markov-modulated Brownian motion $\\{Y(t), \\rho(t)\\}$ with two boundaries at $0$ and $b > 0$, and allow for the controlling Markov chain $\\{\\rho(t)\\}$ to instantaneously undergo a change of phase upon hitting either of the two boundaries at semi-regenerative epochs defined to be the first time the process reaches a boundary since it last hits the other boundary. We call this process a flexible Markov-modulated Brownian motion. Using the recently-established links between stochastic fluid models and Markov-modulated Brownian motions, we determine important characteristics of first exit times of a Markov-modulated Brownian motion from an interval with a regulated boundary. These results allow us to follow a Markov-regenerative approach and obtain the stationary distribution of the flexible process. This highlights the effectiveness of the regenerative approach in analyzing Markov-modulated Brownian motions subject to more general boundary behaviors than the classic regulated boundaries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-07T05:51:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-sided markov-modulated brownian motion",
      "feedback control",
      "instantaneous change",
      "analyzing markov-modulated brownian motions subject",
      "determine important characteristics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160301945L"
    }
  }
}