CLT FOR SEVASTYANOV BRANCHING PROCESSES WITH NON-HOMOGENEOUS IMMIGRATION - Hyrien, Ollivier; Mitov, Kosto V; Yanev, Nickolay M (Journal of applied statistical science, 2013)
Branching processes with immigration have been extensively studied. They were introduced by Sevastyanov, who investigated a class of continuous-time Markov branching processes in which the immigration process was formulated as a time-homogeneous Poisson process. Discrete time branching processes with immigration have been considered later by several authors. Age-dependent branching processes with immigration have also been proposed to describe the temporal development of populations of differentiated cells in vivo. Bellman-Harris branching processes with non-homogeneous Poisson immigration have been considered by Hiryen and Yanev as models of cell proliferation kinetics. In this chapter the authors study a class of Sevastyanov branching processes with an immigration component specified as a nonhomogeneous Poisson process. The development and repair of tissues of the body is controlled by the processes of cell division, cell death, and cell differentiation. Because the outcome of the cell cycle is stochastic, age-dependent branching processes have been proposed to describe the dynamics of cell populations. To date, the Bellman-Harris process has remained the model of choice in such applications.