Functional limit theorems for a decomposable branching process

A decomposable branching Galton-Watson process with two types of particles is considered. It is assumed that the particles of the first type produce particles of the first and second types, and produce them in equal amounts, while particles of the second type produce only particles of the same type. The report highlights functional limit theorems for processes that describe the number of particles of either the first type or the second type in different generations and are considered under the conditions that either the total number of particles of the first type is $N$ or the total number of particles of the second type is greater than $N$ or equal $N \to \infty$.