{
  "id": "0906.3876",
  "version": "v1",
  "published": "2009-06-21T16:12:35.000Z",
  "updated": "2009-06-21T16:12:35.000Z",
  "title": "Markov chains conditioned never to wait too long at the origin",
  "authors": [
    "Saul Jacka"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Motivated by Feller's coin-tossing problem, we consider the problem of conditioning an irreducible Markov chain never to wait too long at 0. Denoting by $\\tau$ the first time that the chain, $X$, waits for at least one unit of time at the origin, we consider conditioning the chain on the event $(\\tau>T)$. We show there is a weak limit as $T\\to \\infty$ in the cases where either the statespace is finite or $X$ is transient. We give sufficient conditions for the existence of a weak limit in other cases and show that we have vague convergence to a defective limit if the time to hit zero has a lighter tail than $\\tau$ and $\\tau$ is subexponential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-21T16:12:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "60J80",
      "60J50",
      "60B10"
    ],
    "keywords": [
      "markov chains",
      "weak limit",
      "fellers coin-tossing problem",
      "first time",
      "lighter tail"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.3876J"
    }
  }
}