带有一个适应σ域族随机环境分枝过程的矩Moments of the Branching Process with Random Environments Adapted to a Family of δ-Fields
武利芳
摘要(Abstract)：
令{Zn}为带有一个适应σ域族{Bn}的随机环境分枝过程,mζn为在Bn条件下子女分布的均值,且mζn几乎必然收敛到mζ.文章主要讨论了{Wn}(Wn=Zm-nn)在L1和L2收敛的充分条件,在这些条件下有:am--n≤EZn≤bm--n,cm--2n≤DZn≤d-m-2n,其中0
关键词(KeyWords)：
随机环境;分枝过程;矩;上鞅
基金项目(Foundation):
作者(Author):
武利芳
参考文献(References)：
- [1]HOWARD WEINER.Moments of The Maximum a Critical Branching Process[J].J.Appl.Prob.,1984,21,920-923.
- [2]KLEBANER F C.Geometric Rate of Growth in Population-size-dependent Branching Processes[J].J.Appl.Prob.,1984,21,40-49.
- [3]HAN-XING WANG,DAFAN FANG.Asymptotic Behavior of Population-size-dependent Branching Processes in Markovian Ran-dom Environments[J].J.Appl.Prob.,1999,30:11-13.