随机环境中线性控制分枝链及其两极分化性质

随机环境中线性控制分枝链及其两极分化性质 The Polarization of Linear Controlled Branching Process in Random Environment 侯传志 HOU Chuan-zhi 1 2 first-author 胡迪鹤 HU Di-he 1 2 武汉大学数学与统计学院 武汉大学数学与统计学院 School of Mathematics and Statistics, Wuhan University School of Mathematics and Statistics, Wuhan University 武汉大学数学与统计学院,湖北,武汉,430072 武汉大学数学与统计学院,湖北,武汉,430072 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. 随机转移矩阵 随机环境中的马氏链 随机环境中线性控制分枝链 生成母函数 随机环境中的随机根树 random transition matrix Markov chain in random environment linear controlled branching process in random environment original generating function random root tree in random environment O211.6 国家自然科学基金（10371092）;武汉大学自强基金资助项目 2004-01-01 2021-04-01 1