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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 316, Pages 222–234
DOI: https://doi.org/10.4213/tm4200 (Mi tm4200) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On the Genealogical Structure of Critical Branching Processes in a Varying Environment

Götz Kersting

Institut für Mathematik, Goethe Universität, Frankfurt am Main, Robert-Mayer-Str. 6-10, 60325 Frankfurt, Germany
Full-text PDF (221 kB) Citations (3)
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DOI: https://doi.org/10.4213/tm4200
Abstract: Critical branching processes in a varying environment behave much the same as critical Galton–Watson processes. In this note we like to confirm this finding with regard to the underlying genealogical structures. In particular, we consider the most recent common ancestor given survival and the corresponding reduced branching processes, in the spirit of Zubkov (1975) and Fleischmann and Siegmund-Schultze (1977).
Keywords: branching process, varying environment, Galton–Watson process, critical process, reduced process, most recent common ancestor, exponential distribution, Yule process.
Received: February 18, 2021
Revised: March 1, 2021
Accepted: August 26, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 316, Pages 209–219
DOI: https://doi.org/10.1134/S0081543822010151
Bibliographic databases:
Document Type: Article
UDC: 519.21
MSC: Primary 60J80
Language: Russian
Citation: Götz Kersting, “On the Genealogical Structure of Critical Branching Processes in a Varying Environment”, 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, 222–234; Proc. Steklov Inst. Math., 316 (2022), 209–219
Citation in format AMSBIB
\Bibitem{Ker22}
\by G\"otz~Kersting
\paper On the Genealogical Structure of Critical Branching Processes in a Varying Environment
\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 222--234
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4200}
\crossref{https://doi.org/10.4213/tm4200}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 316
\pages 209--219
\crossref{https://doi.org/10.1134/S0081543822010151}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129085993}
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    • This publication is cited in the following 3 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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