数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (2): 501-512.doi: 10.1016/S0252-9602(14)60023-0

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CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

高志强|刘全升*|汪和松   

  1. Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China; Univ. Bretagne-Sud, CNRS UMR 6205, LMBA, Campus de Tohannic, F-56000 Vannes, France School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha 410004, China; School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha 410004, China
  • 收稿日期:2012-07-12 修回日期:2013-11-28 出版日期:2014-03-20 发布日期:2014-03-20
  • 通讯作者: 刘全升,quansheng.liu@univ-ubs.fr E-mail:gaozq@bnu.edu.cn;quansheng.liu@univ-ubs.fr;hesongwang@tom.com
  • 基金资助:

    The project is partially supported by the National Natural Science Foundation of China (NSFC, 11101039, 11171044, 11271045), a cooperation program between NSFC and CNRS of France (11311130103), the Fundamental Research Funds for the Central Universities, and Hunan Provincial Natural Science Foundation of China (11JJ2001).

CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

 GAO Zhi-Qiang, LIU Quan-Sheng*, WANG He-Song   

  1. Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China; Univ. Bretagne-Sud, CNRS UMR 6205, LMBA, Campus de Tohannic, F-56000 Vannes, France School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha 410004, China; School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha 410004, China
  • Received:2012-07-12 Revised:2013-11-28 Online:2014-03-20 Published:2014-03-20
  • Contact: LIU Quan-Sheng,quansheng.liu@univ-ubs.fr E-mail:gaozq@bnu.edu.cn;quansheng.liu@univ-ubs.fr;hesongwang@tom.com
  • Supported by:

    The project is partially supported by the National Natural Science Foundation of China (NSFC, 11101039, 11171044, 11271045), a cooperation program between NSFC and CNRS of France (11311130103), the Fundamental Research Funds for the Central Universities, and Hunan Provincial Natural Science Foundation of China (11JJ2001).

摘要:

We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi-ronment is supposed to be independent and identically distributed. For A (R, let Zn(A) be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn(·) with appropriate normalization.

关键词: Branching random walk, random environment in time, central limit theorems

Abstract:

We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi-ronment is supposed to be independent and identically distributed. For A (R, let Zn(A) be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn(·) with appropriate normalization.

Key words: Branching random walk, random environment in time, central limit theorems

中图分类号: 

  • 60J10