Some asymptotic results for the branching process with immigration

C. Z. Wei and J. Winnicki

Stochastic Processes and their Applications, 1989, vol. 31, issue 2, 261-282

Abstract: Motivated 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 is examined and found to depend on whether the process is transient or recurrent. Some convergence theorems for the supercritical case are also included.

Date: 1989
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