(untitled) (Международный научный журнал «Инженер», 2026)
Many scientific and practical studies conducted on a global scale, in most cases, are reduced to the problems of studying branching random processes. The theory of branching random processes with particle interaction studies the laws of evolution of a population of particles, in which the reproduction of new particles occurs through the interaction of several particles already existing in the population. Branching processes with particle interaction are of great importance in scientific fields such as demography, medicine, chemistry, biology, as well as genetic coding and population management. In the paper, we investigate the asymptotic behavior of branching random processes with interaction of particles. A direct equation is obtained for the generating function of the process . Also, a limit theorem for the moment of the -th order of branching random process with interaction of particles is obtained.