随机环境中两性分枝过程的极限性质  

Limiting behaviors of bisexual branching processes in random environments

作　　者：李应求[1] 胡杨利[1] 张影[1] 

机构地区：[1]长沙理工大学数学与计算科学学院,长沙410114

出　　处：《中国科学：数学》2015年第5期611-622,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11171044);湖南省自然科学基金(批准号:11JJ2001和13JJ6048);湖南省高等学校科研基金(批准号:14B010)资助项目

摘　　要：在随机环境两性分枝过程中,本文引入每个配对单元的条件均值增长率,讨论它的性质,得到了过程的条件均值的上、下界,研究了过程由此上、下界规范化后的极限性质.特别地,本文还研究了各代雄性、雌性个体数适当规范化后的极限性质,建立了过程与各代雄性、雌性个体数规范化后的等价定理.For a bisexual branching process in a random environment, the conditional mean growth rate per mating unit is introduced, and its related properties are studied, then the upper and lower bounds of conditional mean of the process are obtained. The limiting behaviors of the number of mating units in each generation normalized by these two bounds are respectively investigated. Particularly, the limiting behaviors of the number of females and males in each generation normalized by slightly modified bounds are discussed too, and equivalence theorems between the normalized number of mating units and that of females or males in each generation are obtained.

关 键 词：随机环境 两性分枝过程 几乎处处收敛 L1-收敛 

分 类 号：O211.65[理学—概率论与数理统计]