Harmonic moments and large deviations for supercritical branching processes with immigration

doi:10.1007/s11464-017-0642-3

Front. Math. China

2017, Vol. 12

Issue (5) : 1201-1220 https://doi.org/10.1007/s11464-017-0642-3

RESEARCH ARTICLE

Harmonic moments and large deviations for supercritical branching processes with immigration

Qi SUN, Mei ZHANG(

)

School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, China

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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.

Keywords Supercritical branching processes harmonic moments large deviations immigration

Corresponding Author(s): Mei ZHANG

Issue Date: 30 September 2017

Cite this article:

Qi SUN,Mei ZHANG. Harmonic moments and large deviations for supercritical branching processes with immigration[J]. Front. Math. China, 2017, 12(5): 1201-1220.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0642-3
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I5/1201

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