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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 316, Pages 145–168
DOI: https://doi.org/10.4213/tm4212 (Mi tm4212) 		 
This article is cited in 2 scientific papers (total in 2 papers)

A Scaling Limit Theorem for Galton–Watson Processes in Varying Environments

Rongjuan Fanga, Zenghu Lib, Jiawei Liub

a College of Mathematics and Informatics, Fujian Normal University, Fuzhou, 350007, China
b Laboratory of Mathematics and Complex Systems (MOE), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China
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DOI: https://doi.org/10.4213/tm4212
Abstract: 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.
Funding agency Grant number
National Key Research and Development Program of China 2020YFA0712900
National Natural Science Foundation of China 11531001
Program for Probability and Statistics: Theory and Application IRTL1704
Program for Innovative Research Team in Science and Technology in Fujian Province University IRTSTFJ
Education and Scientific Research Project for Young and Middle-aged Teachers in Fujian Province of China JAT200072
This work is supported by the National Key R&D Program of China (no. 2020YFA0712900), the National Natural Science Foundation of China (no. 11531001), the Program for Probability and Statistics: Theory and Application (no. IRTL1704), the Program for Innovative Research Team in Science and Technology in Fujian Province University (no. IRTSTFJ) and the Education and Scientific Research Project for Young and Middle-aged Teachers in Fujian Province of China (no. JAT200072).
Received: May 10, 2021
Revised: May 26, 2021
Accepted: November 10, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 316, Pages 137–159
DOI: https://doi.org/10.1134/S0081543822010114
Bibliographic databases:
Document Type: Article
UDC: 519.218.2+519.214.6
Language: Russian
Citation: Rongjuan Fang, Zenghu Li, Jiawei Liu, “A Scaling Limit Theorem for Galton–Watson Processes in Varying Environments”, Branching Processes and Related Topics, Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin, Trudy Mat. Inst. Steklova, 316, Steklov Math. Inst., Moscow, 2022, 145–168; Proc. Steklov Inst. Math., 316 (2022), 137–159
Citation in format AMSBIB
\Bibitem{FanLiLiu22}
\by Rongjuan~Fang, Zenghu~Li, Jiawei~Liu
\paper A Scaling Limit Theorem for Galton--Watson Processes in Varying Environments
\inbook Branching Processes and Related Topics
\bookinfo Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 316
\pages 145--168
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4212}
\crossref{https://doi.org/10.4213/tm4212}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 316
\pages 137--159
\crossref{https://doi.org/10.1134/S0081543822010114}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129062857}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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