Geodesic
On application of slowly varying functions with remainder in the theory of Galton--Watson branching process
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 1, pp. 51-57

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We investigate an application of slowly varying functions (in sense of Karamata) in the theory of Galton–Watson branching processes. Consider the critical case so that the generating function of the per-capita offspring distribution has the infinite second moment, but its tail is regularly varying with remainder. We improve the Basic Lemma of the theory of critical Galton-Watson branching processes and refine some well-known limit results.
Keywords: Galton–Watson branching process, slowly varying functions, generating functions. 
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     author = {Azam A. Imomov and Erkin E. Tukhtaev},
     title = {On application of slowly varying functions with remainder in the theory of {Galton--Watson} branching process},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Azam A. Imomov; Erkin E. Tukhtaev. On application of slowly varying functions with remainder in the theory of Galton--Watson branching process. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 1, pp. 51-57. http://geodesic.mathdoc.fr/item/JSFU_2019_12_1_a3/