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

07/03/2023

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by   Hao Wu, et al.

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Let (Z_n)_n≥ 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≥ 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.