ON LARGE DEVIATION RATES FOR SUMS ASSOCIATED WITH GALTON-WATSON PROCESSES

被引：14

作者：

He, Hui ^{[1
,2
]}

机构：

[1] Beijing Normal Univ, Beijing 100875, Peoples R China

[2] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing 100875, Peoples R China

来源：

ADVANCES IN APPLIED PROBABILITY | 2016年 / 48卷 / 03期

关键词：

Galton-Watson process; domain of attraction; stable distribution; slowly varying function; large deviation; Lotka-Nagaev estimator; Schroder constant; SUPERCRITICAL BRANCHING-PROCESSES; MIGRATING BINOMIAL OBSERVATIONS; INDEPENDENT RANDOM-VARIABLES; RANDOM-WALKS; PROBABILITIES; DOMAIN;

D O I：

10.1017/apr.2016.22

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Given a supercritical Galton-Watson process {Z(n)} and a positive sequence {epsilon(n}) we study the limiting behaviors of P(S-Zn /Z(n) >= epsilon(n)) with sums S-n of independent and identically distributed random variables X-i and m = E[Z(1)]. We assume that we are in the Schroder case with EZ(1) log Z(1) < infinity and X-1 is in the domain of attraction of an alpha-stable law with 0 < alpha < 2. As a by-product, when Z(1) is subexponentially distributed, we further obtain the convergence rate of Z(n+1)/Z(n) to m as n -> infinity.

引用

页码：672 / 690

页数：19

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