On the Distribution of the Number of Final Particles in a Branching Process with Transformations and Pairwise Interactions

Abstract

A Markov continuous time branching process with two types of particles $T_1$ and $T_2$ is considered. Particles of the two types appear either as the offspring of a particle of type $T_1$, or as a result of interaction of two particles of type $T_1$. Under certain restrictions on the distribution of the number of new particles the asymptotic behavior of the expectation and variance of the number of particles of the two types are investigated and the asymptotic normality of the distribution of the number of final particles of type $T_2$ is established when the initial number of particles of type $T_1$ is large.