数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1105-1114.doi: 10.1016/S0252-9602(10)60108-7

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SOME PROPERTIES OF GALTON-WATSON BRANCHING PROCESSES IN VARYING ENVIRONMENTS

余旌胡1, 许芳2   

  1. 1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, China
     State Key Laboratory of Software Engineering, Wuhan University, Wuhan 430072, China; 2. Wuhan Institute of Physics and Mathematics, |the Chinese Academy of Sciences, Wuhan 430071, China
     Graduate School of the Chinese Academy of Sciences, |Beijing 100039, China
  • 收稿日期:2007-12-30 修回日期:2008-07-10 出版日期:2010-07-20 发布日期:2010-07-20
  • 基金资助:

    This article are supported by NNSF of China (60534080, 70571079) and Open Fundation of SKLSE of Wuhan University (2008-07-03)

SOME PROPERTIES OF GALTON-WATSON BRANCHING PROCESSES IN VARYING ENVIRONMENTS

 YU Jing-Hu1, XU Fang2   

  1. 1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, China
     State Key Laboratory of Software Engineering, Wuhan University, Wuhan 430072, China; 2. Wuhan Institute of Physics and Mathematics, |the Chinese Academy of Sciences, Wuhan 430071, China
     Graduate School of the Chinese Academy of Sciences, |Beijing 100039, China
  • Received:2007-12-30 Revised:2008-07-10 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    This article are supported by NNSF of China (60534080, 70571079) and Open Fundation of SKLSE of Wuhan University (2008-07-03)

摘要:

This article deals with some properties of Galton-Watson branching processes in varying environments. A
necessary and sufficient condition for relative recurrent state is presented, and a series of ratio limit properties of the transition probabilities are showed.

关键词: Branching processes, varying environments, non-homogeneous, relative recurrent, transition probability, ratio theorem

Abstract:

This article deals with some properties of Galton-Watson branching processes in varying environments. A
necessary and sufficient condition for relative recurrent state is presented, and a series of ratio limit properties of the transition probabilities are showed.

Key words: Branching processes, varying environments, non-homogeneous, relative recurrent, transition probability, ratio theorem

中图分类号: 

  • 60Q17