{
  "id": "0912.1928",
  "version": "v1",
  "published": "2009-12-10T07:40:44.000Z",
  "updated": "2009-12-10T07:40:44.000Z",
  "title": "Conditional limit theorems for regulated fractional Brownian motion",
  "authors": [
    "Hernan Awad",
    "Peter Glynn"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AAP605 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2009, Vol. 19, No. 6, 2102-2136",
  "doi": "10.1214/09-AAP605",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value $b$, we provide the limiting distribution for the amount of time that the workload process spends above level $b$ over the busy cycle straddling the origin, as $b\\to\\infty$. Our results can be interpreted as showing that long delays occur in large clumps of size of order $b^{2-1/H}$. The conditional limit result involves a finer scaling of the queueing process than fluid analysis, thereby departing from previous related literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-10T07:40:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25",
      "90B22",
      "68M20",
      "60F99"
    ],
    "keywords": [
      "regulated fractional brownian motion",
      "conditional limit theorems",
      "fractional brownian motion input",
      "stationary fluid queue",
      "conditional limit result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1928A"
    }
  }
}