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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 $\alpha \in (1,2)$. The limit law is the ratio of two dependent stable random variables with indices $\alpha/2$ and $2\alpha/3$, respectively, and it has a continuously differentiable density function... (read more)
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