A critical branching process with immigration which evolves in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the population, we investigate the tail distribution of the so-called life period of the process, i.e. the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time.

中文翻译：

---

移民在零时停止的随机环境中的分支过程

考虑了在随机环境中演变的具有移民的关键分支过程。假设在人口中没有个体的情况下不允许移民，我们研究所谓进程的生命周期的尾部分布，即进程启动时刻之间的时间间隔长度为正数粒子数和种群中第一次没有个体的时刻。