Recurrence of Markov branching processes with immigration

We derive criteria for assessing the recurrence and positive-recurrence of Markov branching processes with immigration. Although our method is designed to tackle the instantaneous immigration case investigated in Chen and Renshaw (1990), this new approach can also be applied to the stable immigration case previously considered by Yamazato (1975) and others.Markov branching process instantaneous immigration stable immigration recurrence positive-recurrence