Harmonic moments and large deviations for supercritical branching processes with immigration

Abstract

We study the convergence rates of the harmonic moments for supercritical branching processes with immigration Z_n, extending the previous results for non-immigration cases in literature. As a by-product, the large deviations for Z_n+1/Z_n are also studied. We can see that there is a phase transition in converging rates depending on the generating functions of both branching and immigration.

Key words： Supercritical; branching processes; harmonic moments; large deviations; immigration

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