"Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences
Slavtchova-Bojkova M., Hyrien, O., Yanev, N. M. Poisson Random Measures and Noncritical Multitype Markov Branching Processes. Comptes rendus de l’Académie bulgare des Science, 74, 5, "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2021, DOI: 10.7546/CRABS.2021.03.04, 658-668
Comptes rendus de l’Académie bulgare des Science;74(5)
We investigate noncritical multi-type Markov branching processes with immigration generated by Poisson measures. Limiting distributions are obtained when the rates of the Poisson measures are asymptotically equivalent to exponential or regularly varying functions. In particular, results analogous to a strong LLN are presented, and limiting normal distributions are obtained when the rates increase. When the rates decrease, then conditional limiting distributions are established. A stationary limiting distribution is obtained when the mean Poisson measure grows linearly. The asymptotic behaviour of the first and second moments of the processes is also investigated.