Limiting Distributions in Branching Processes with Two Types of Particles

Let us consider a decomposable e branching process with two types of particles T₁, T₂ such that particles of type T₂ can only produce particles of types T₁ whereas particles of type T₁ can produce particles of both types. The aim of this paper is to characterize the kind of distribution of the particles of types T₁ and T₂ when the total number n of all particles is fixed. Especially we are interested in the limit case n — ∞. It turns out that depending on the parameters of the process a number of different limiting distributions, e.g. normal or x2 distributions, appear.