{
  "id": "0710.3269",
  "version": "v2",
  "published": "2007-10-17T11:22:01.000Z",
  "updated": "2008-04-23T13:11:56.000Z",
  "title": "Differential equation approximations for Markov chains",
  "authors": [
    "R. W. R. Darling",
    "J. R. Norris"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/07-PS121 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Probability Surveys 2008, Vol. 5, 37-79",
  "doi": "10.1214/07-PS121",
  "categories": [
    "math.PR"
  ],
  "abstract": "We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is emphasised. The general theory is illustrated in three examples: the classical stochastic epidemic, a population process model with fast and slow variables, and core-finding algorithms for large random hypergraphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-23T13:11:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65",
      "60J75",
      "05C80"
    ],
    "keywords": [
      "markov chain",
      "differential equation approximations",
      "large random hypergraphs",
      "population process model",
      "general theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.3269D"
    }
  }
}