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arXiv · 2307.01084

Wasserstein-$1$ distance and nonuniform Berry-Esseen bound for a supercritical branching process in a random environment

Hao Wu·Xiequan Fan·Zhiqiang Gao·Yinna Ye
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Abstract

Let $ (Z_{n})_{n\geq 0} $ be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-$1$ distance for the process $ (Z_{n})_{n\geq 0} $, which completes a result of Grama et al. [Stochastic Process. Appl., 127(4), 1255-1281, 2017]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size $Z_n$ are discussed.

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Hao Wu, Xiequan Fan, Zhiqiang Gao, Yinna Ye. 2023-07-03. Wasserstein-$1$ distance and nonuniform Berry-Esseen bound for a supercritical branching process in a random environment. https://doi.org/10.3770/j.issn%3A2095-2651.2023.06.009

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