数学物理学报(英文版)

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THE CONSTRUCTION OF MULTITYPE CANONICAL MARKOV BRANCHING CHAINS IN RANDOM ENVIRONMENTS

胡迪鹤   

  1. 武汉大学数学与统计学院, 武汉 430072
  • 收稿日期:2004-04-10 修回日期:2005-04-15 出版日期:2006-07-20 发布日期:2006-07-20
  • 通讯作者: 胡迪鹤
  • 基金资助:

    Project supported by the National Natural Science Foundation of China
    and the Foundation of Wuhan University.

THE CONSTRUCTION OF MULTITYPE CANONICAL MARKOV BRANCHING CHAINS IN RANDOM ENVIRONMENTS

Hu Dihe   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2004-04-10 Revised:2005-04-15 Online:2006-07-20 Published:2006-07-20
  • Contact: Hu Dihe

摘要:

The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the
concepts of the multitype canonical Markov branching chain in random
environment (CMBCRE) and multitype Markov branching chain in random
environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.

关键词: Random Markov matrix, Markov chain in random environment, Markov branching chain in random environment, canonical Markov branchingchain in random environment, generator random variables

Abstract:

The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the
concepts of the multitype canonical Markov branching chain in random
environment (CMBCRE) and multitype Markov branching chain in random
environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.

Key words: Random Markov matrix, Markov chain in random environment, Markov branching chain in random environment, canonical Markov branchingchain in random environment, generator random variables

中图分类号: 

  • 60J05