{
  "id": "0812.4556",
  "version": "v3",
  "published": "2008-12-24T17:38:25.000Z",
  "updated": "2010-10-21T08:41:25.000Z",
  "title": "Uniform convergence for complex $[\\mathbf{0,1}]$-martingales",
  "authors": [
    "Julien Barral",
    "Xiong Jin",
    "Benoît Mandelbrot"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AAP664 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 2010, Vol. 20, No. 4, 1205-1218",
  "doi": "10.1214/09-AAP664",
  "categories": [
    "math.PR"
  ],
  "abstract": "Positive $T$-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We focus on martingales constructed on the interval $T=[0,1]$ and replace random measures by random functions. We specify a large class of such martingales for which we provide a general sufficient condition for almost sure uniform convergence to a nontrivial limit. Such a limit yields new examples of naturally generated multifractal processes that may be of use in multifractal signals modeling.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-10-21T08:41:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "martingale",
      "model intermittent turbulence",
      "replace random measures",
      "general sufficient condition",
      "sure uniform convergence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4556B"
    }
  }
}