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.

引用

页码：51 / 57

页数：7

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