随机环境中的两性Galton-Watson分枝过程的极限行为

作者:马世霞;李晋枝 刊名:南开大学学报:自然科学版 上传者:陈诺

【摘要】考虑了后代概率分布受一个独立同分布环境过程所控制的两性Galton-Watson分枝过程,得到了有关过程渐进增长的若干结果.

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第 44卷 第 3期 2011年 6月 南 开 大 学 学 报(自然科学版 ) Acta Scientiarum N aturalium Universitatis N ankaiensis Vo1.44 N.O3 Jun.2011 Article ID:0465—7942(2011)03—0035—05 The Limit Behavior for the Bisexua1 Gahon—W atson Branching Processes in Random Environments Ma Shixia ,Li Jinzhi (1。School of Science,Hebei University of Technology,Tianjin 300401,China; 2.College of Science,Central University for Nationalities。Beijing 100081,China) Abstract:A bisexual Gahon—W atso . n branching process is considered,where the offspring probability dis— tribution is controlled by an independent and identically environment process.Some results for the asymptotic growth associated with the process are obtained. Key words:bisexual Gahon-W atson limit behavior CLC number:O211.65 0 Intr0duction branching processes I branching processes in random environments; Doeum ent code:A The bisexual Gahon—W atson branching process (abbreviated as BGW P)which is as an important two—type branching model has received much attention in the literature(see references E1—63.).Re— cently,some modified BGW P such as BGW P with immigration and BGW P in varying environments(see references[7l oJ)have been investigated.For this kinds of models,extinction problem and limit prob— ability behavior have been studied.In this paper we consider a more general bisexual branching model called the bisexual Galton—W atson process in random environments(abbreviated as BGW PRE)in which the offspring distribution law change stochastically with an in

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