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arXiv · 2312.12847

Moments of Mandelbrot cascades at critical exponents

Yong Han·Yanqi Qiu·Zipeng Wang
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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.

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Yong Han, Yanqi Qiu, Zipeng Wang. 2023-12-20. Moments of Mandelbrot cascades at critical exponents. https://arxiv.org/abs/2312.12847

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