Reducible branching processes: theory and applications

Peter Olofsson

Department of Statistics, Rice University, Houston, USA

Abstract

Assuming a multi-type branching process to be irreducible leads to the well known characteristics of exponential growth and stable type composition. When the irreducibility assumption is relaxed, the process can exhibit quite a different behavior. We survey some of the theory for reducible branching processes and investigate some applications where such processes naturally arise.