{
  "id": "0910.0324",
  "version": "v2",
  "published": "2009-10-02T04:50:12.000Z",
  "updated": "2010-05-27T20:03:51.000Z",
  "title": "Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes",
  "authors": [
    "Xia Chen",
    "Wenbo V. Li",
    "Jan Rosinski",
    "Qi-Man Shao"
  ],
  "comment": "To appear in the Annals of Probability",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes. We also show that a fractional Brownian motion and the related Riemann-Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of our large deviation estimates, we derive laws of iterated logarithm for the corresponding local times. The key points of our methods: (1) logarithmic superadditivity of a normalized sequence of moments of exponentially randomized local time of a fractional Brownian motion; (2) logarithmic subadditivity of a normalized sequence of moments of exponentially randomized intersection local time of Riemann-Liouville processes; (3) comparison of local and intersection local times based on embedding of a part of a fractional Brownian motion into the reproducing kernel Hilbert space of the Riemann-Liouville process.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-27T20:03:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60J55",
      "60F10",
      "60G15",
      "60G18"
    ],
    "keywords": [
      "fractional brownian motion",
      "riemann-liouville processes",
      "normalized sequence",
      "large deviation estimates",
      "riemann-liouville process behave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.0324C"
    }
  }
}