Exact Convergence Rate of the Local Limit Theorem for a Branching Random Walk in Zd with a Random Environment in Time

Jian-xin LIU ¹Zhi-qiang GAO²

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作者信息

1. School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China
2. Laboratory of Mathematics and Complex Systems (Ministry of Education),School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China
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Abstract

Consider a branching random walk with a random environment in time in the d-dimensional integer lattice.The branching mechanism is governed by a supercritical branching process,and the particles perform a lazy random walk with an independent,non-identical increment distribution.For A ⊂ Zd,let Zn(A)be the number of offsprings of generation n located in A.The exact convergence rate of the local limit theorem for the counting measure Zn(·)is obtained.This partially extends the previous results for a simple branching random walk derived by Gao(2017,Stoch.Process Appl.).

Key words

Branching random walk/Random environment/Local limit theorems/Exact convergence rate

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基金项目

National Natural Science Foundation of China(11971063)

出版年

2024

数学年刊B辑(英文版)

国家教育部委托复旦大学主办

数学年刊B辑(英文版)

CSTPCD

影响因子：0.129

ISSN：0252-9599

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