On Application of Slowly Varying Functions with Remainder in the Theory of Galton-Watson Branching Process

被引：3
|
作者：
Imomov, Azam A. [1 ,2 ]
Tukhtaev, Erkin E. [2 ]
机构：
[1] Cabinet Ministers Republ Uzbekistan, State Testing Ctr, 12 Bogishamol St, Tashkent 100202, Uzbekistan
[2] Karshi State Univ, 17 Kuchabag St, Karshi City 180100, Uzbekistan
来源：
JOURNAL OF SIBERIAN FEDERAL UNIVERSITY-MATHEMATICS & PHYSICS | 2019年 / 12卷 / 01期
关键词：
Galton-Watson branching process; slowly varying functions; generating functions;
D O I：
10.17516/1997-1397-2019-12-1-51-57
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：51 / 57
页数：7
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