Critical branching processes in a sparse random environment

Abstract

We introduce a branching process in a sparse random environment as an intermediate model between a Galton–Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and prove Yaglom-type limit theorems, that is, limit theorems for the size of population conditioned on the survival event.

Keywords

• Branching process
• functional limit theorem
• random environment
• survival probability