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