{
  "id": "2007.11390",
  "version": "v1",
  "published": "2020-07-22T12:53:55.000Z",
  "updated": "2020-07-22T12:53:55.000Z",
  "title": "The asymptotic tails of limit distributions of continuous time Markov chains",
  "authors": [
    "Chuang Xu",
    "Mads Christian Hansen",
    "Carsten Wiuf"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions of continuous-time Markov chains on a subset of the non-negative integers. A new identity for stationary measures is established. In particular, for continuous-time Markov chains with asymptotic power-law transition rates, tail asymptotics for stationary distributions are classified into three types by three easily computable parameters: (i) Conley-Maxwell-Poisson distributions (light-tailed), (ii) exponential-tailed distributions, and (iii) heavy-tailed distributions. Similar results are derived for quasi-stationary distributions. The approach to establish tail asymptotics is different from the classical semimartingale approach. We apply our results to biochemical reaction networks (modeled as continuous-time Markov chains), a general single-cell stochastic gene expression model, an extended class of branching processes, and stochastic population processes with bursty reproduction, none of which are birth-death processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-22T12:53:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "60J28",
      "60J74",
      "90E20"
    ],
    "keywords": [
      "continuous time markov chains",
      "continuous-time markov chains",
      "asymptotic tails",
      "limit distributions",
      "tail asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}