Exact convergence rate of the local limit theorem for a branching random walk in a time-dependent random environment on d-dimensional integer lattice

Zhiqiang Gao and Xiaoyan Zhang

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 4, 988-1011

Abstract: Consider a branching random walk in Zd, where both the offspring distribution and the displacement law vary with generation time. For each x∈Zd, let Zn(x) denote the number of particles of n-th generation located at x. We derive exact convergence rate of the local limit theorem for the counting measure Zn(x). This generalizes the result obtained in Gao (2017, SPA) by adding the random environment affects, and improves it by weakening the moment condition required for the offspring distribution.

Date: 2023
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DOI: 10.1080/03610926.2021.1921807

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