2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108939This paper demonstrates a new regeneration processes technology making use of positive stable distributions. We study the asymptotic behavior of branching processes with a randomly controlled migration component. Using the new method, we confirm some known results and establish new limit theorems that hold in a more general setting.Probability60K05, 60J80text