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Statistical inference of subcritical strongly stationary Galton--Watson processes with regularly varying immigration
Matyas Barczy, Bojan Basrak, Péter Kevei, Gyula Pap, Hrvoje Plan · 2019-10-03 · via math.ST updates on arXiv.org

We describe the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton--Watson processes with regularly varying immigration with tail index $α\in (1,2)$. The limit law is the ratio of two dependent stable random variables with indices $α/2$ and $2α/3$, respectively, and it has a continuously differentiable density function. We use point process technique in the proofs.

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