{
  "id": "math/0608311",
  "version": "v3",
  "published": "2006-08-13T07:41:16.000Z",
  "updated": "2009-12-08T13:35:23.000Z",
  "title": "Upcrossing inequalities for stationary sequences and applications",
  "authors": [
    "Michael Hochman"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AOP460 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2009, Vol. 37, No. 6, 2135-2149",
  "doi": "10.1214/09-AOP460",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "For arrays $(S_{i,j})_{1\\leq i\\leq j}$ of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process $(S_{1,n})_{n=1}^{\\infty}$ can be bounded in terms of a measure of the ``mean subadditivity'' of the process $(S_{i,j})_{1\\leq i\\leq j}$. We derive universal upcrossing inequalities with exponential decay for Kingman's subadditive ergodic theorem, the Shannon--MacMillan--Breiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-12-08T13:35:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "37A35",
      "60G10",
      "60G17",
      "94A17",
      "68Q30"
    ],
    "keywords": [
      "stationary sequences",
      "applications",
      "kingmans subadditive ergodic theorem",
      "kolmogorov complexity",
      "random variables"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8311H"
    }
  }
}