Geodesic
A Scaling Limit Theorem for Galton--Watson Processes in Varying Environments
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching Processes and Related Topics, Tome 316 (2022), pp. 145-168

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We prove a scaling limit theorem for discrete Galton–Watson processes in varying environments. A simple sufficient condition for the weak convergence in the Skorokhod space is given in terms of probability generating functions. The limit theorem gives rise to the continuous-state branching processes in varying environments studied recently by several authors.
Keywords: Galton–Watson processes, continuous state, varying environments, probability generating functions, scaling limits. 
@article{TM_2022_316_a10,
     author = {Rongjuan Fang and Zenghu Li and Jiawei Liu},
     title = {A {Scaling} {Limit} {Theorem} for {Galton--Watson} {Processes} in {Varying} {Environments}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {145--168},
     publisher = {mathdoc},
     volume = {316},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2022_316_a10/}
}
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Rongjuan Fang; Zenghu Li; Jiawei Liu. A Scaling Limit Theorem for Galton--Watson Processes in Varying Environments. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching Processes and Related Topics, Tome 316 (2022), pp. 145-168. http://geodesic.mathdoc.fr/item/TM_2022_316_a10/