摘要
引进了随机环境中线性控制分枝链的概念,讨论了各类母函数的关系,并用生成母函数精确表达了其他母函数;采用图论的方法,引进了随机根树,随机环境中的随机根树,以及随机环境中控制随机根树等一系列的概念,证明了它们分别与分枝链,随机环境中的分枝链,及随机环境中的控制分枝链的一一对应关系,在此基础上得到了随机环境中线性控制分枝链的两极分化性质.
The definition of linear controlled branching process in random environment is introduced, and the relations of all kinds of generating functions are studied. The original generating function is used to show the others exactly. We use the method of graph theory to introduce the following definitions: random root tree, random root tree in random environment, and the controlled random root tree in random environment.Base on these, we prove the polarization of linear controlled branching process in random environment.
出处
《武汉大学学报（理学版）》
CAS
CSCD
北大核心
2004年第1期6-10,共5页
Journal of Wuhan University:Natural Science Edition
基金
国家自然科学基金(10371092)
武汉大学自强基金资助项目
关键词
随机转移矩阵
马氏链
线性控制分枝链
生成母函数
随机根树
两极分化
random transition matrix
Markov chain in random environment
linear controlled branching process in random environment
original generating function
random root tree in random environment
