Exact convergence rate in central limit theorem for a supercritical branching process with immigration in a random environment

Abstract

Let {Zn} be a supercritical branching process with immigration in an independent, identically distributed(i.i.d.) environment ξ. The Berry-Esseen bound for log⁡Zn has been established by Wang et al. (2021). To refine that, under the less restrictive moment conditions, we calculate the exact convergence rate in the central limit theorem for log⁡Zn under the annealed law.