{
  "id": "2001.00134",
  "version": "v1",
  "published": "2020-01-01T03:43:37.000Z",
  "updated": "2020-01-01T03:43:37.000Z",
  "title": "Inverse Problems for Ergodicity of Markov Chains",
  "authors": [
    "Zhi-Feng Wei"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "For both continuous-time and discrete-time Markov Chains, we provide criteria for inverse problems of classical types of ergodicity: (ordinary) erogodicity, algebraic ergodicity, exponential ergodicity and strong ergodicity. Our criteria are in terms of the existence of solutions to inequalities involving the $Q$-matrix (or transition matrix $P$ in time-discrete case) of the process. Meanwhile, these criteria are applied to some examples and provide \"universal\" treatment, including single birth processes and several multi-dimensional models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-01T03:43:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "60J10",
      "60J75",
      "82C22"
    ],
    "keywords": [
      "inverse problems",
      "discrete-time markov chains",
      "single birth processes",
      "multi-dimensional models",
      "strong ergodicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}