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.
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Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant No. 11371061).
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Sun, Q., Zhang, M. Harmonic moments and large deviations for supercritical branching processes with immigration. Front. Math. China 12, 1201–1220 (2017). https://doi.org/10.1007/s11464-017-0642-3
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DOI: https://doi.org/10.1007/s11464-017-0642-3