Functional limit theorems for the decomposable branching process with two types of particles

A decomposable Galton – Watson process with two types of particles is considered. Particles of the first type produce equal random numbers of particles of both types, particles of the second type produce particles of the second type only. Under the condition that the total number of the first type particles is equal to $N$ the functional limit theorems are proved for the numbers of particles of both types existing at times of the orders of $\sqrt{N}$, of $N$ and of the intermediate orders. \def\acknowledgementname{Funding