Decomposition of supercritical linear-fractional branching processes
  It is well known that a supercritical single-type Bienyam\'e-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienyam\'e-Galton-Watson processes with countably many types. 
Serik Sagitov and Altynay Shaimerdenova
math.PR