Critical Branching Regenerative Processes with Migration
  This 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. 
George P. Yanev, Kosto V. Mitov, and Nickolay M. Yanev