Harmonic moments, large and moderate deviation principles for Mandelbrot’s cascade in a random environment

Yingqiu Li, Quansheng Liu and Xuelian Peng

Statistics & Probability Letters, 2019, vol. 147, issue C, 57-65

Abstract: For Mandelbrot’s cascade in a random environment, we find the critical value for the existence of harmonic moments of the limit variable of Mandelbrot’s martingale, and establish large and moderate deviation principles for the free energy. As applications, we show the corresponding limit theorems for branching random walks in random environments.

Keywords: Mandelbrot’s cascade; Branching random walk; Random environment; Harmonic moments; Large deviations; Moderate deviations (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2018.10.002

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