{
  "id": "2312.12847",
  "version": "v1",
  "published": "2023-12-20T08:55:54.000Z",
  "updated": "2023-12-20T08:55:54.000Z",
  "title": "Moments of Mandelbrot cascades at critical exponents",
  "authors": [
    "Yong Han",
    "Yanqi Qiu",
    "Zipeng Wang"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We obtain the asymptotic growth rate of the moments of the Mandelbrot random cascades at critical exponents. The key ingredient is a $q$ to $q/2$ reduction method for the moment-estimation, which is obtained by combining the martingale inequalities due to Burkholder and Burkholder-Rosenthal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-20T08:55:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponents",
      "mandelbrot cascades",
      "asymptotic growth rate",
      "mandelbrot random cascades",
      "reduction method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}