Acta mathematica scientia,Series B ›› 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

 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)

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

CLC Number: 

  • 60Q17
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