随机环境下具有控制函数的两性分枝模型(英文)

作者:马建静 邢永胜 刊名:南开大学学报:自然科学版 上传者:李智

【摘要】研究了一类在随机环境下具有控制函数的一类两性分枝过程.证明了在控制函数满足适当的条件时,证明了个体平均增长率极限存在,且基于此极限,给出了该过程灭绝概率为1的充要条件.

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第 48卷 第 2期 2015年 4月 南 开 大 学 学 报(自然科学版) Acta Scientiarum Naturalium Universitatis N口 kn 咒 s Vo1.48 N_O2 Apr.2015 Article ID:0465—7942(2015)02—0031—04 Two-sex Branch M ode1 with Contro1 Function in Random Environment Ma Jianjing,Xing Y0ngsheng (College of Mathematics and Information Sciences,Shando’2g Instit“t已of B s ss口,z Technology,Yantai 264005,China) Abstract;One class of bisexual Gahon—W atson branching processes with control function in rand0m envi— ronment is studied·Under a suitable assumption on the control function,the limit of mean growth rate per mat— ing unit exists,and based on the limit,a criterion i given to identify whether or n0t the pr0cess admit s uItimate extinct with probability one. Key words:bisexual Galton—Watson branching processes;control function;environment process ;extinc— tion probability CLC number:0211.6 0 Intr0duction Document code:A The bisexual branching processes have received much attention in the literature(see references E1—— 5 1)· It can be stated that significant efforts have been made regarding random or varying environment models(see references E6"1 O]). In this paper,we are interested in one class of bisexual Gahon—W atson Process whose offspring and mating functions influenced by the number of couples . The model can be deftned as foilows. On a probability space(O,3-,P),The random rector{( , ) )satimy: (F州, 1)=∑( m ), =0,1,⋯, Z 一 (F , +1), = 0,1,⋯ . (1) wnere the empty sum is considered to be (O,0).The ran

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