论文标题
在不同环境中移民的分支过程的再生
Regeneration of branching processes with immigration in varying environments
论文作者
论文摘要
在本文中，我们考虑了在不同环境中移民的某些线性分支分支过程。对于$ n \ ge0，$ let $ z_n $计数$ n $ th代的个人数量，不包括在时间$n。$n。$ n. $ n $的移民中，如果$ z_n = 0，我们将$ n $称为$ n $。然后，我们构建了一些具体的例子，以表现出由所谓的不同环境引起的奇怪现象。该过程可能灭绝，但只有许多再生时间有限。另外，当有无限的再生时间时，我们表明，对于每个$ \ varepsilon> 0，$ [0，n] $中的再生时间数不超过$（\ log n）^{1+\ varepsilon} $ as $ n \ rightarrow \ rightarrow \ rightarrow \ rightarrow \ $ infty。$ infty。$。
In this paper, we consider certain linear-fractional branching processes with immigration in varying environments. For $n\ge0,$ let $Z_n$ counts the number of individuals of the $n$-th generation, which excludes the immigrant which enters into the system at time $n.$ We call $n$ a regeneration time if $Z_n=0.$ We give first a criterion for the finiteness or infiniteness of the number of regeneration times. Then, we construct some concrete examples to exhibit the strange phenomena caused by the so-called varying environments. It may happen that the process is extinct but there are only finitely many regeneration times. Also, when there are infinitely many regeneration times, we show that for each $\varepsilon>0,$ the number of regeneration times in $[0,n]$ is no more than $(\log n)^{1+\varepsilon}$ as $n\rightarrow\infty.$
