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

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

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 53; no. 23; pp. 8412 - 8427
Main Authors Li, Yingqiu, Tang, Xinping, Wang, Hesong
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.12.2024
Taylor & Francis Ltd
Subjects
Branching processes with immigration
central limit theorem
Convergence
exact convergence rate
random environment
Theorems
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Summary:Let {Z n } be a supercritical branching process with immigration in an independent, identically distributed(i.i.d.) environment ξ. The Berry-Esseen bound for log⁡Z n 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⁡Z n under the annealed law.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2023.2288792