Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case

被引：5

作者：

Wachtel, V. I. ^{[1
]}

Denisov, D. E. ^{[2
]}

Korshunov, D. A. ^{[3
]}

机构：

[1] Univ Munich, Math Inst, D-80333 Munich, Germany

[2] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[3] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2013年 / 282卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

LARGE DEVIATIONS;

D O I：

10.1134/S0081543813060205

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

As is well known, for a supercritical Galton-Watson process Z (n) whose offspring distribution has mean m > 1, the ratio W (n) := Z (n) /m (n) has almost surely a limit, say W. We study the tail behaviour of the distributions of W (n) and W in the case where Z (1) has a heavy-tailed distribution, that is, for every lambda > 0. We show how different types of distributions of Z (1) lead to different asymptotic behaviour of the tail of W (n) and W. We describe the most likely way in which large values of the process occur.

引用

页码：273 / 297

页数：25

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D. A. Korshunov
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