May 2024 Berry-Esseen bound and Cramér moderate deviation expansion for a supercritical branching random walk
Thi Thuy Bui, Ion Grama, Quansheng Liu
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Bernoulli 30(2): 1401-1415 (May 2024). DOI: 10.3150/23-BEJ1636

Abstract

We consider a supercritical branching random walk where each particle gives birth to a random number of particles of the next generation, which move on the real line, according to a fixed law. Let Zn be the counting measure which counts the number of particles of n-th generation situated in a given region. Under suitable conditions, we establish a Berry-Esseen bound and a Cramér type moderate deviation expansion for Zn with suitable norming.

Funding Statement

The work has been supported by the Centre Henri Lebesgue (CHL, ANR-11-LABX-0020- 01), and the National Natural Science Foundation of China (Grants Nos. 11971063 and 12271062).

Acknowledgements

Quansheng Liu is the corresponding author.

Citation

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Thi Thuy Bui. Ion Grama. Quansheng Liu. "Berry-Esseen bound and Cramér moderate deviation expansion for a supercritical branching random walk." Bernoulli 30 (2) 1401 - 1415, May 2024. https://doi.org/10.3150/23-BEJ1636

Information

Received: 1 November 2021; Published: May 2024
First available in Project Euclid: 31 January 2024

MathSciNet: MR4699557
Digital Object Identifier: 10.3150/23-BEJ1636

Keywords: Berry-Esseen bound , branching processes , Branching random walk , central limit theorem , large and moderate deviations , Random walks

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Vol.30 • No. 2 • May 2024
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