Statistica Sinica 1(1991), 175-184

CONVERGENCE RATES FOR THE CRITICAL

BRANCHING PROCESS WITH IMMIGRATION

C. Z. Wei

University of Maryland and Academia Sinica

Abstract: For a critical branching process with immigration, {X_n},(logX_n)/log n is shown to converge almost surely to 1 when {X_n} is transient. The rates of growth for and are then derived and used to obtain convergence rates for the conditional weighted least squares estimators of the generation and immigration means.

Key words and phrases: Branching process with immigration, convergence rate, martingale, conditional least squares.