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arXiv · 1301.6840

Small value probabilities for supercritical branching processes with immigration

Weijuan Chu·Wenbo V. Li·Yan-Xia Ren
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Abstract

We consider a supercritical Galton-Watson branching process with immigration. It is well known that under suitable conditions on the offspring and immigration distributions, there is a finite, strictly positive limit ${\mathcal{W}}$ for the normalized population size. Small value probabilities for ${\mathcal{W}}$ are obtained. Precise effects of the balance between offspring and immigration distributions are characterized.

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Weijuan Chu, Wenbo V. Li, Yan-Xia Ren. 2014-02-05. Small value probabilities for supercritical branching processes with immigration. https://doi.org/10.3150/12-bej490

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