Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (1): 282-305.

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A Second Order Correction of the Local Limit Theorem for a Branching Random Walk with a Random Environment in Time on ${\mathbb{Z}}^d$

Zhiqiang Gao()   

  1. Laboratory of Mathematics and Complex Systems(Ministry of Education) & School of Mathematical Sciences, Beijing Normal University, Beijing 100875
  • Received:2019-12-25 Online:2022-02-26 Published:2022-02-23
  • Supported by:
    the NSFC(11971063)

Abstract:

Consider a branching random walk on ${\mathbb{Z}}^d$ with a random environment in time, where the branching offspring distribution and the migration law change as times goes by. Under the mild moment conditions, we derive the second order expansion for $Z_n(z)$, which counts the number of particles of generation $n$ at $z\in {\mathbb{Z}}^d$.

Key words: Branching random walk, Local limit theorem, Asymptotic expansions

CLC Number: 

  • O211.6
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