Models of random processes with particle interaction

Abstract

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.