{
  "id": "1202.0952",
  "version": "v3",
  "published": "2012-02-05T11:00:22.000Z",
  "updated": "2012-06-14T15:35:33.000Z",
  "title": "Explosion, implosion, and moments of passage times for continuous-time Markov chains: a semimartingale approach",
  "authors": [
    "Mikhail Menshikov",
    "Dimitri Petritis"
  ],
  "comment": "33 pages",
  "doi": "10.1016/j.spa.2014.03.001",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We establish general theorems quantifying the notion of recurrence --- through an estimation of the moments of passage times --- for irreducible continuous-time Markov chains on countably infinite state spaces. Sharp conditions of occurrence of the phenomenon of explosion are also obtained. A new phenomenon of implosion is introduced and sharp conditions for its occurrence are proven. The general results are illustrated by treating models having a difficult behaviour even in discrete time.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-14T15:35:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60K20"
    ],
    "keywords": [
      "passage times",
      "semimartingale approach",
      "sharp conditions",
      "irreducible continuous-time markov chains",
      "countably infinite state spaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.0952M"
    }
  }
}