{
  "id": "1403.0716",
  "version": "v3",
  "published": "2014-03-04T08:59:54.000Z",
  "updated": "2014-11-21T02:24:41.000Z",
  "title": "Some asymptotic formulae for Bessel process",
  "authors": [
    "Yuu Hariya"
  ],
  "comment": "The content of Section 3 in the second version has been modified so that it gives sharp asymptotics for remainder terms",
  "categories": [
    "math.PR"
  ],
  "abstract": "We recover in part a recent result of Hamana-Matsumoto (2014) on the asymptotic behaviors for tail probabilities of first hitting times of Bessel process. Our proof is based on a weak convergence argument. The same reasoning enables us to derive the asymptotic behaviors for the tail probability of the time at which the global infimum of Bessel process is attained, and for expected values relative to local infima. In addition, we give another proof of the result of Hamana-Matsumoto with improvement of error estimates, which complements in the case of noninteger dimensions the asymptotic formulae by van den Berg (2007) for first hitting times of multidimensional Brownian motion.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-17T08:31:45.000Z",
      "abstract": "We recover in part a recent result of Hamana-Matsumoto (2014) on the asymptotic behaviors for tail probabilities of first hitting times of Bessel process. Our proof is based on a weak convergence argument. The same reasoning enables us to derive the asymptotic behaviors for the tail probability of the time at which the global infimum of Bessel process is attained, and for expected values relative to local infima. Some relevant results are also presented. In addition, we give another proof of the result of Hamana-Matsumoto with improvement of error estimates.",
      "comment": "Asymptotic error estimates added in an extra section with slight change in abstract and introduction",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-11-21T02:24:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60B10"
    ],
    "keywords": [
      "bessel process",
      "asymptotic formulae",
      "asymptotic behaviors",
      "tail probability",
      "weak convergence argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.0716H"
    }
  }
}