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Mathematics > Probability
Title: Wasserstein-$1$ distance and nonuniform Berry-Esseen bound for a supercritical branching process in a random environment
(Submitted on 3 Jul 2023 (v1), last revised 4 Dec 2023 (this version, v2))
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.
Submission history
From: Yinna Ye [view email][v1] Mon, 3 Jul 2023 15:06:21 GMT (21kb)
[v2] Mon, 4 Dec 2023 08:15:39 GMT (21kb)
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