Geodesic
On the Genealogical Structure of Critical Branching Processes in a Varying Environment
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching Processes and Related Topics, Tome 316 (2022), pp. 222-234

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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. 
@article{TM_2022_316_a14,
     author = {G\"otz Kersting},
     title = {On the {Genealogical} {Structure} of {Critical} {Branching} {Processes} in a {Varying} {Environment}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {222--234},
     publisher = {mathdoc},
     volume = {316},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2022_316_a14/}
}
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Götz Kersting. On the Genealogical Structure of Critical Branching Processes in a Varying Environment. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching Processes and Related Topics, Tome 316 (2022), pp. 222-234. http://geodesic.mathdoc.fr/item/TM_2022_316_a14/