Some asymptotic results for the branching process with immigration

AbstractMotivated by the statistical applications, the asymptotic behavior of certain functionals of a branching process with immigration, {Xn}, is studied. The main results concern the critical case. A functional limit theorem for X[nt]|n is established. The rate of growth for Tn=Σi=0n−1 (Xi+1)−1 is examined and found to depend on whether the process is transient or recurrent. Some convergence theorems for the supercritical case are also included