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 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 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
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
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