This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and emigration is reviewed in detail. Critical controlled branching processes with continuous state space are also discussed.
Yanev, George, "Critical Controlled Branching Processes And Their Relatives" (2015). Mathematical and Statistical Sciences Faculty Publications and Presentations. 39.
Pliska Studia Mathematica