首页|Exact Convergence Rate of the Local Limit Theorem for a Branching Random Walk in Zd with a Random Environment in Time
Exact Convergence Rate of the Local Limit Theorem for a Branching Random Walk in Zd with a Random Environment in Time
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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.).
Branching random walkRandom environmentLocal limit theoremsExact convergence rate
Jian-xin LIU、Zhi-qiang GAO
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School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China
Laboratory of Mathematics and Complex Systems (Ministry of Education),School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China
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