A Functional Limit Theorem for Decomposable Branching Processes with Two Particle Types

A decomposable Galton–Watson branching process with two particle types is studied. It is assumed that the particles of the first type produce equal numbers of particles of the first and second types, while the particles of the second type produce only particles of their own type. Under the condition that the total number of particles of the second type is greater than $N\to \infty$, a functional limit theorem for the process describing the number of particles of the first type in different generations is proved.