Critical Controlled Branching Processes and Their Relatives

TL;DR

This survey reviews critical controlled branching processes, including discrete and continuous state space models, focusing on their behaviors under various immigration and emigration regimes, and summarizes key theoretical results.

Contribution

It compiles and presents comprehensive results on critical controlled branching processes, highlighting recent developments and different regimes of immigration and emigration.

Findings

Analysis of critical migration regimes

Results on continuous state space processes

Summary of key theoretical properties

Abstract

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.