The Stationary Distribution of a Branching Process Allowing Immigration: A Remark on the Critical Case
The Stationary Distribution of a Branching Process Allowing Immigration: A Remark on the Critical Case
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允许移民的分支过程的平稳分布：对关键案例的评论
DOI：
10.1111/j.2517-6161.1968.tb01516.x
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发表时间：
1968
期刊：
影响因子：
--
通讯作者：
E. Seneta
中科院分区：
文献类型：
--
作者：
E. Seneta
摘要对于一个分支过程，其中个体从一代到一代地繁殖，就像在高尔顿-沃森过程中一样，并且在每一代都受到移民分量的影响，已知有时存在平稳极限分布。特别是，如果每个个体的后代的平均数小于1，并且移民分布是合理的，这是如此。我们表明，这样的分布可能存在，即使当平均数的后代是团结，在特殊的情况下，我们给出了充分的条件。
SummaryFor a branching process in which the individuals reproduce from generation to generation as in a Galton‐Watson process, and are also subject to an immigration component at each generation, it is known that a stationary‐limiting distribution sometimes exists. In particular, this is so if the mean number of offspring per individual is less than unity and the immigration distribution is reasonably behaved. We show that such a distribution may exist even when the mean number of offspring is unity, under special circumstances for which we give sufficient conditions.