随机环境中伴有移民两性分枝过程的极限性质  

The Limit Properties of the Bisexual Branching Process with Population-size-dependent Immigration in Random Environments

作　　者：宋明珠[1] 

机构地区：[1]铜陵学院数学与计算机系,安徽铜陵244000

出　　处：《应用数学》2012年第3期667-671,共5页Mathematica Applicata

基　　金：高校省级自然科学研究项目(kj2009B096);高校省级优秀青年人才基金项目(2011SQRL143);教育部人文社科青年基金项目(12YJCZH217)

摘　　要：本文在独立同分布的随机环境下,建立带有移民的两性分枝过程{Zn}n≥0,且移民人口数依赖当前人口数,证得{Zn}n≥0和{(Fn,Mn)}n≥1是随机环境中的马氏链,并得到第n代每个配对单元平均增长率{rk}k≥0的极限性质,从而推广了经典两性分枝过程的相关理论.In this paper, we consider a bisexual branching process with population-size-de- pendent immigration in independent and identically distributed random environments. It is proved the bisexual branching process is Markov chains in random environments and the double chains about the number of females and males in the nth generation is double Markov chains in random environments, too. The limit unit is studied. Some limit properties known random environments are enlarged. properties of the mean growth rate per mating about classical bisexual branching process in

关 键 词：随机环境 两性分枝过程 移民依赖人口数 马氏链 极限性质 

分 类 号：O211.65[理学—概率论与数理统计]