arXiv Open Access 2022

Central limit theorem and Berry-Esseen bounds for a branching random walk with immigration in a random environment

Chunmao Huang Yukun Ren Runze Li

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Abstrak

We consider a branching random walk on $d$-dimensional real space with immigration in a time-dependent random environment. Let $Z_n(\mathbf t)$ be the so-called partition function of the process, namely, the moment generating function of the counting measure describing the dispersion of individuals at time $n$. For $\mathbf t$ fixed, the logarithm $\log Z_n(\mathbf t)$ satisfies a central limit theorem. By studying the logarithmic moments of the intrinsic submartingale of the system and its convergence rates, we establish the uniform and non-uniform Berry-Esseen bounds corresponding to the central limit theorem, and discover the exact convergence rate in the central limit theorem.

Topik & Kata Kunci

math.PR

Penulis (3)

Chunmao Huang

Yukun Ren

Runze Li

Format Sitasi

APA MLA BibTeX

Huang, C., Ren, Y., Li, R. (2022). Central limit theorem and Berry-Esseen bounds for a branching random walk with immigration in a random environment. https://arxiv.org/abs/2210.08157

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓