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Let (Zn) be a branching process with immigration in an independent andidentically distributed random environment. Under necessary moment conditions,we show the exact convergence rate in the central limit theorem on logZn byusing the convergence rates of the logarithm of submartingale and the result ofthe corresponding random walk on the Berry-Esseen bound.

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