Ergodic properties of subcritical multitype Galton–Watson processes with immigration

In the paper ergodic properties of multitype Galton–Watson processes are investigated in the subcritical case without further regularity assumptions. Sufficient and necessary conditions for the existence of the stationary distribution and its moments are provided. Under moment conditions geometric ergodicity and rate of converge for the moments of the process are proved. Geometric properties of the Markovian class structure are also studied.