Regeneration of Critical Multi-Type Branching Process with Immigration

In this paper, we study a two-type linear fractional branching process with immigration. For n ≥ 0, let Z_n = (Z_n,1, Z_n,2)⊤ denote the population size of the nth generation excluding immigrants arriving at time n. We call time n as a regeneration epoch if Z_n = 0. In the critical case, we derive the limiting distribution of regeneration counts up to time n.