Branching processes Immigration Poisson process Limit theorems
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 22, No 1, (2013), 57p-70p
The paper proposes an extension of Sevastyanov (1957) model allowing an immigration in the moments of a homogeneous Poisson process. Markov branching processes with time-nonhomogeneous Poisson immigration are considered as models in cell proliferation kinetics and limit theorems are proved in the supercritical case. Some of the limiting results can be interpreted as generalizations of the classical result of Sevastyanov (1957) and new effects are obtained due to the non-homogeneity.