Non Homogeneous Decomposable Branching Processes

Abstract

In this paper, a non-homogeneous, decomposable and continuous-time Markov branching process with three types of particles has been considered. Assume that the first type of particles are immutable, particles of the second type may transmute into particles of the second and third types and particles of the third type only into those of the third type and probabilities of these transmutations are independent of time. This process can be considered as a two-type decomposable branching process with time-dependent immigration. Some limit theorems are proved for the number of particles, when reproduction processes are critical and intensities of the number of “immigrants” are decreasing.