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arXiv · 2609.18503

Functional limit theorems for Galton--Watson processes with inhomogeneous immigration

Matyas Barczy·Dániel Bezdány
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Abstract

We study the asymptotic behavior of a sequence of Galton--Watson processes with inhomogeneous immigration when the limit of the means of the offspring distributions is less than $1$ or equal to $1$. Under growth conditions on the expected values of the immigration distributions and the variances of the offspring distributions, and assuming the weak convergence of properly scaled immigration processes towards a non-negative stochastic process $\mathcal Y$ with càdlàg or continuous sample paths, we establish functional limit theorems for the sequence of Galton--Watson processes with inhomogeneous immigration in question. The limit stochastic processes can be represented as a constant multiple or an integral functional of $\mathcal Y$.

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Matyas Barczy, Dániel Bezdány. 2026-09-16. Functional limit theorems for Galton--Watson processes with inhomogeneous immigration. https://arxiv.org/abs/2609.18503

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