LIMIT THEOREMS FOR SUPERCRITICAL MARKOV BRANCHING PROCESSES WITH NON-HOMOGENEOUS POISSON IMMIGRATION

This paper deals with Markov branching processes allowing immigration at random time points described by a non-homogeneous Poisson process. This class of processes generalizes a classical model proposed by Sevastyanov, which included a time-homogeneous Poisson immigration. The proposed model finds applications in cell kinetics studies. Limit theorems are obtained in the supercritical case. Some of these results extend the classical results derived by Sevastyanov, others offer novel insights as a result of the non-homogeneity of the immigration process.