Critical branching processes with infinite variance and increasing immigration
Theorems are stated and proved on the asymptotic behaviour in distribution of the population size for a critical branching process with time-homogeneous family size distribution with regularly varying tail and infinite variance, in which there is time-inhomogeneous immigration with expected number of immigrants in a generation tending to infinity in a regularly varying manner. Universal families of laws emerge from the limiting behaviour.
time-homogeneous family size distribution
scientific article; zbMATH DE number 589637