EXPONENTIAL RATE OF ALMOST-SURE CONVERGENCE OF INTRINSIC MARTINGALES IN SUPERCRITICAL BRANCHING RANDOM WALKS

被引：12

作者：

Iksanov, Alexander ^{[1
]}

Meiners, Matthias ^{[1
]}

机构：

[1] Natl Taras Shevchenko Univ Kyiv, Fac Cybernet, UA-01033 Kiev, Ukraine

来源：

JOURNAL OF APPLIED PROBABILITY | 2010年 / 47卷 / 02期

关键词：

Branching random walk; martingale; rate of convergence; renewal theory; THEOREM;

D O I：

10.1239/jap/1276784906

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：

We provide sufficient conditions which ensure that the intrinsic martingale in the supercritical branching random walk converges exponentially fast to its limit. We include in particular the case of Galton-Watson processes so that our results can be seen as a generalization of a result given in the classical treatise by Asmussen and Hering (1983). As an auxiliary tool, we prove ultimate versions of two results concerning the exponential renewal measures which may be of interest in themselves and which correct, generalize, and simplify some earlier works.

引用

页码：513 / 525

页数：13

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