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| Exact Convergence Rate of the Local Limit Theorem for aBranching Random Walk in Zd with a RandomEnvironment in Time |
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Citation： |
Jian-xin LIU,Zhi-qiang GAO.Exact Convergence Rate of the Local Limit Theorem for aBranching Random Walk in Zd with a RandomEnvironment in Time[J].Chinese Annals of Mathematics B,2024,45(5):805~822 |
| Page view： 92
Net amount： 76 |
Authors： |
Jian-xin LIU; Zhi-qiang GAO |
Foundation： |
by the National Natural Science Foundation of China (No. 11971063) |
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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.). |
Keywords： |
Branching random walk, Random environment, Local limit theorems,
Exact convergence rate |
Classification： |
60F05, 60J10, 60G50, 60J80 |
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