Year: 2026
Type: preprint
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 $\mathcal Y$ .
Source: arXiv (Cornell University)
Authors: Barczy, Matyas, Bezdány, Dániel
Institutions: University of Szeged, Hungarian Research Network
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213498646