Geodesic
Critical Galton-Watson branching processes with a~countable set of types and infinite second moments
Sbornik. Mathematics, Tome 212 (2021) no. 1, pp. 1-24

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We consider an indecomposable Galton-Watson branching process with a countable set of types. Assuming that the process is critical and may have infinite variance of the offspring sizes of some (or all) types of particles we describe the asymptotic behaviour of the survival probability of the process and establish a Yaglom-type conditional limit theorem for the infinite-dimensional vector of the number of particles of all types. Bibliography: 20 titles.
Keywords: critical Galton-Watson branching processes with a countable set of types, survival probability, infinite second moments of offspring sizes, regularly varying functions
Mots-clés : Yaglom-type limit theorem. 
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V. A. Vatutin; E. E. Dyakonova; V. A. Topchii. Critical Galton-Watson branching processes with a~countable set of types and infinite second moments. Sbornik. Mathematics, Tome 212 (2021) no. 1, pp. 1-24. http://geodesic.mathdoc.fr/item/SM_2021_212_1_a0/