{
  "id": "1608.03257",
  "version": "v1",
  "published": "2016-08-10T19:04:33.000Z",
  "updated": "2016-08-10T19:04:33.000Z",
  "title": "Detecting Markov Chain Instability: A Monte Carlo Approach",
  "authors": [
    "Michel Mandjes",
    "Brendan Patch",
    "Neil Walton"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We devise a Monte Carlo based method for detecting whether a non-negative Markov chain is stable for a given set of parameter values. More precisely, for a given subset of the parameter space, we develop an algorithm that is capable of deciding whether the set has a subset of positive Lebesgue measure for which the Markov chain is unstable. The approach is based on a variant of simulated annealing, and consequently only mild assumptions are needed to obtain performance guarantees. The theoretical underpinnings of our algorithm are based on a result stating that the stability of a set of parameters can be phrased in terms of the stability of a single Markov chain that searches the set for unstable parameters. Our framework leads to a procedure that is capable of performing statistically rigorous tests for instability, which has been extensively tested using several examples of standard and non-standard queueing networks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-10T19:04:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "detecting markov chain instability",
      "monte carlo approach",
      "single markov chain",
      "non-negative markov chain",
      "non-standard queueing networks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}