A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications

Chunhua Ma

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arXiv · 0906.2586

A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications

Chunhua Ma

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Abstract

We prove a general fluctuation limit theorem for Galton-Watson branching processes with immigration. The limit is a time-inhomogeneous OU type process driven by a spectrally positive Levy process. As applications of this result, we obtain some asymptotic estimates for the conditional least-squares estimator of the offspring means and variances of the offspring and immigration distributions.

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Chunhua Ma. 2009-09-12. A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications. https://arxiv.org/abs/0906.2586

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