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 Zd

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 Zd 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 Zn(z), which counts the number of particles of generation n at zZd.

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

CLC Number: 

  • O211.6
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