Abstract We consider critical Sevastyanov branching processes with immigration at random time-points generated by a Poisson random measure with a local intensity for some slowly varying function The asymptotic behavior of the probability of non-extinction is studied and conditional limiting distributions of the processes with proper normalization are obtained.

中文翻译：

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泊松随机测度和临界 Sevastyanov 分支过程

摘要 我们考虑在随机时间点移民的临界 Sevastyanov 分支过程，该过程由具有局部强度的泊松随机测度生成，用于某些缓慢变化的函数。研究了非灭绝概率的渐近行为，并研究了过程的条件限制分布得到归一化。